
	Where results make sense

Topic: Edge coloring

Related Topics

List edge coloring

Chromatic number

Graph coloring

Petersen graph

Topologist

Sather programming language

Optic neuritis

Lower explosive limit

Karl Guthe Jansky

Caron

Goodyear Tire Company

George William Ross

World Prayer Center

Tenryu

Krystal Steal

	MINIMUM EDGE COLORING
		A coloring of E, i.e., a partition of E into disjoint sets
		Cardinality of the coloring, i.e., the number of disjoint sets
		The maximization variation in which the input is extended with a positive integer k, and the problem is to find the maximum number of consistent vertices over all edge-colorings with k colors, is approximable within e/(e-1) [
	www.nada.kth.se /~viggo/wwwcompendium/node18.html (91 words)

	Edge coloring - Wikipedia, the free encyclopedia
		In graph theory, as with its vertex counterpart, an edge coloring of a graph, when mentioned without any qualification, is always assumed to be a proper coloring of the edges, meaning no two adjacent edges are assigned the same color.
		A proper edge coloring with k colors is called a (proper) k-edge-coloring and is equivalent to the problem of partitioning the edge set into k matchings.
		The smallest number of colors needed in a (proper) edge coloring of a graph G is the chromatic index, or edge chromatic number, χ′(G), also sometimes notated χ
	en.wikipedia.org /wiki/Edge_coloring (372 words)

	Vertex Coloring (Site not responding. Last check: 2007-11-03)
		A coloring of the vertices of this graph assigns the variables to classes such that two variables with the same color do not clash and so can be assigned to the same register.
		Such a coloring of the vertices of a bipartite graph means that the graph can be drawn with the red vertices on the left and the blue vertices on the right such that all edges go from left to right.
		Color interchange is a win in terms of producing better colorings, at a cost of increased time and implementation complexity.
	www2.toki.or.id /book/AlgDesignManual/BOOK/BOOK4/NODE178.HTM (1427 words)

	15. Planarity and Coloring
		If we add an edge between two vertices, then e and f each increase by 1 if there is a path in G between the ends of the new edge.
		Now we start from the neighbor vertex with color A and mark all its neighbors of color C and all their neighbors of color A and theirs of color C until all vertices that can be reached from that neighbor by going only on vertices of color A and C are marked.
		This coloring can fail only if one of the graphs for a connected component is complete of degree d and the other is the triangle containing v1 v2 and vn.
	www-math.mit.edu /18.310/planarity_coloring.html (2392 words)

	Citations: and Roman Sot'ak - Cern'y, Horn'ak (ResearchIndex) (Site not responding. Last check: 2007-11-03)
		Edge coloring The observability of a graph G is the least number of colors in a proper edge coloring of G such that the color sets at vertices of G (sets of colors of their incident edges) are pairwise distinct.
		A set balanced k edge coloring of a graph G is a proper k edge coloring of G such that for each vertex degree d each d set of colors appears at bn d = Gamma k d Delta c or dn d = Gamma k d Delta e vertices,....
		They defined the observability of a graph G, written obs(G) to be the least number of colors in a proper edge coloring of G such that the color sets at vertices of G (sets of colors of their incident edges) are pairwise distinct.
	citeseer.ist.psu.edu /context/1320677/0 (277 words)

	Marx Dániel publikációi (Site not responding. Last check: 2007-11-03)
		The sum of a coloring is the sum of the colors assigned to the vertices (assuming that the colors are the positive integers).
		The edge multicoloring problem is that given a graph G and integer demands x(e) for every edge e, assign a set of x(e) colors to edge e, such that adjacent edges have disjoint sets of colors.
		In the minimum sum edge coloring problem we have to assign positive integers to the edges of a graph such that adjacent edges receive different integers and the sum of the assigned numbers is minimal.
	www.cs.bme.hu /~dmarx/publikacio-reszletes.html (2383 words)

	[No title]
		The edge-coloring problem consists of partitioning the edges of a graph G into the minimum number of disjoint subsets such that all edges in a given subset are not adjacent.
		However, as the density, (which is the ratio of the number of edges to the number of vertices in a graph), increased, the performance of his approach faltered, producing approximations using as many as three additional colors beyond the optimal number.
		Note the range of valid colors for the remaining edges is reduced by the colors of edges connected to the node with the highest degree.
	euler.mcs.utulsa.edu /~rogerw/papers/Enochs-GECCO-2001.doc (2688 words)

	1.5.8 Edge Coloring (Site not responding. Last check: 2007-11-03)
		Excerpt from The Algorithm Design Manual: The edge coloring of graphs arises in a variety of scheduling applications, typically associated with minimizing the number of noninterfering rounds needed to complete a given set of tasks.
		The color classes represent the different time periods in the schedule, with all meetings of the same color happening simultaneously.
		To gain insight into edge coloring, note that a graph consisting of an even-length cycle can be edge-colored with 2 colors, while odd-length cycles have an edge-chromatic number of 3.
	www.cs.sunysb.edu /~algorith/files/edge-coloring.shtml (336 words)

	List edge-coloring - Wikipedia, the free encyclopedia
		In mathematics, list edge-coloring is a type of graph coloring.
		More precisely, a list edge-coloring is a choice function that maps every edge to a color from a prescribed list for that edge.
		The edge choosability, or list edge colorability, list edge chromatic number, or list chromatic index, ch′(G) of a graph G is the least number k such that G is k-edge-choosable.
	en.wikipedia.org /wiki/List_edge-coloring (183 words)

	CU CSCI Thesis Defense - Skulrattanakulchai (2002-2003)
		A proper coloring of a graph is a partition of its elements in such a way that no two adjacent or incident elements belong to the same set in the partition.
		It is a vertex coloring, an edge coloring, or a total coloring, according as the elements to be partitioned are the vertices alone, the edges alone, or both the vertices and edges, respectively.
		A list coloring is a proper coloring subject to an extra condition that a color to be assigned to an element must come from that element's set (``list'') of colors priorly associated with that element as part of the input.
	www.cs.colorado.edu /events/defenses/2002-2003/skulrattanakulchai.html (371 words)

	archivist on the edge
		This sock was actually done for about 24 hours and then Lolly saw it and mentioned how small my feet were...no, my feet are not as small as I hoped they were when I "finished" the sock.
		This burnt orange coloring in this absolute perfect yarn (which I was pretty much blissuflly unaware of until Ashley dangled the carrot (or icicle) in front of blogland.
		I got a skein of Dream in color (the choclately one) sock yarn, Lolly got the green Dream in Color worsted and some lovely lace weight dyed in California, it's pretty, see for yourself.
	www.archivistontheedge.com (2350 words)

	Edge Coloring (Site not responding. Last check: 2007-11-03)
		Discussion: The edge coloring of graphs arises in a variety of scheduling applications, typically associated with minimizing the number of noninterfering rounds needed to complete a given set of tasks.
		Any edge coloring problem on G can be converted to the problem of finding a vertex coloring on the line graph L(G), which has a vertex of L(G) for each edge of G and an edge of L(G) if and only if the two edges of G share a common vertex.
		Although any edge coloring problem can be so formulated as a vertex coloring problem, this is usually a bad idea, since the edge coloring problem is easier to solve.
	www2.toki.or.id /book/AlgDesignManual/BOOK/BOOK4/NODE179.HTM (693 words)

	Edge Coloring (Site not responding. Last check: 2007-11-03)
		Edge coloring a graph means assigning colors to edges so that adjacent edges get different colors, using the minimum number of colors in the process.
		Although it is known that every graph G can be edge colored with at most Delta(G)+1 colors, and that at least Delta(G) colors are always necessary, it is NP-hard to decide between these two consecutive integers.
		My main objective is to study edge coloring in interval graphs and related classes.
	www.ic.unicamp.br /~meidanis/research/edge (448 words)

	3 Algorithm Description
		In both cases, the three paths and the disjoint cycles are colored by reusing some of the colors that appear on pre-colored edges of the gadget (no new colors are required).
		The proof of Lemma 1 considers, for football-shaped gadgets as well as for dumbbell-shaped gadgets, all possible arrangements of colors on the pre-colored edges of H and explains, for each configuration, how the colors d, s, and s' can be used to color the three paths and the remaining cycles of the gadget.
		In these gadgets there is no preserved double color that can be reused without worrying about other triplets; however, with the additional assumption that the relevant pre-colored edges are not parallel, it is possible to reuse some of the double colors without creating conflicts with the colorings of other triplets.
	www.jea.acm.org /ARTICLES/Vol4Nbr4/node3.html (2851 words)

	Coloring R/C Aircraft
		The best color scheme for beginners that I have found is a combination of large starburst patterns on top of the wing and horizontal stabilizer, and a solid dark color underneath the wing and horizontal stabilizer.
		The base color of the top of the wing must be a very light color such as white, yellow or some other very light color The starburst pattern starts out at the center of the wing, from 3/8" under the wing leading edge to about 1" back from the leading edge at the top.
		The leading edge red or orange pie slice is wrapped around the leading edge so that it has the maximum area of visibility when edge on.
	www.ultimatecharger.com /color.html (2349 words)

	variant of graph edge coloring - Science Math Combinatorics (Site not responding. Last check: 2007-11-03)
		I have come across a variant of graph edge coloring in some research I have been doing, and am trying to determine if the problem has been studied before.
		the one addition is that each edge has a lower bound, which restricts the range of colors that can be assigned to that edge (so, if we number colors 0,1,2,..., an edge with a bound of 2, cannot use colors 0 or 1).
		the one addition is that each edge has a > lower bound, which restricts the range of colors > that can be assigned to that edge (so, if we number > colors 0,1,2,..., an edge with a bound of 2, cannot > use colors 0 or 1).
	www.okka.biz /variant_of_graph_edge_coloring-1846855-283-a.html (424 words)

	Research
		Edge colorings of graphs, Research seminar of the college of basic and applied sciences, October 15, 2003
		Coloring edges of graphs embedded in a surface of Euler characteristic —3, CombinaTexas 04, April 9-10, 2004, Texas AandM University
		Edge colorings of graphs with small average degree, AMS meeting in Orlando, November 9-10.
	www.mtsu.edu /~rluo/research.htm (557 words)

	About the Graph (Site not responding. Last check: 2007-11-03)
		A total coloring is one in which each edge and each vertex is assigned a color, such that no co-incident edges receive the same color, no adjacent vertices receive the same color, and no vertex receives the same color as an incident edge.
		The coloring of this graph is not optimal since it is possible to achieve a total coloring with fewer colors.
		On the other hand, if the simple sequential vertex coloring algorithm is applied to this graph, with the pairs of vertices of the same color being first in the input, then four colors will be used.
	web.cs.ualberta.ca /%7Ejoe/Coloring/about.html (254 words)

	COMPUTER SCIENCE TECHNICAL REPORT ABSTRACTS (Site not responding. Last check: 2007-11-03)
		The required number of colors is called the chromatic index of the graph.
		We consider the edge coloring problem in the framework of the relationship between an integer program and its linear programming relaxation.
		To do this we first formulate edge coloring as an integer program and we define the fractional chromatic index to be the optimum of its linear programming relaxation.
	reports-archive.adm.cs.cmu.edu /anon/1998/abstracts/98-176.html (259 words)

	[No title]
		The present main result is an O(k+n) algorithm for k- coloring a maximum cradinality subset of the intervals, assuming that the endpoints of the intervals are presorted.
		These fractional coloring procedures are then used for generating upper bounds for the (weighted or unweighted) maximum clique problem in the framework of a branch-and-bound procedure.
		Graph coloring with adaptive evolutionary algorithms Eiben, A.E.,Leiden University, NL-2300 RA Leiden, Netherlands,Hauw, J.K. van der and Hemert, J.I. vanJournal of Heuristics, vol: 4, Mar 1998, 1, page(s): 25-46 This paper presents the results of an experimental investigation on solving graph coloring problems with Evolutionary Algorithms (EAs).
	mat.gsia.cmu.edu /COLOR02/BIB/international-abstracts-in-or.doc (2713 words)

	Distributional Graph Edge Coloring
		We distinguish the tiles by coloring the corners of the tiles.
		When a self-loop is colored, it is convenient to simply say that the looped node is colored (with the same color of the self-loop).
		, are the toroidal edges and the edge
	www.uncg.edu /mat/acc-forum/avgnp/node31.html (1741 words)

	André Kündgen's Research (Site not responding. Last check: 2007-11-03)
		The face-hypergraph of a graph G embedded on a surface has the same vertex-set as G and every face of G corresponds to an edge of the face-hypergraph consisting of the vertices incident to the face.
		A hypergraph is weakly k-colorable (weakly k-choosable) if there is a coloring of its vertices from a set of k colors (from every assignment of lists of size k to its vertices) such that no edge is monochromatic.
		Thus a weak coloring of a face-hypergraph corresponds to a vertex coloring of the underlying graph such that no face is monochromatic.
	www.csusm.edu /akundgen/papers/facehyper.abs.html (169 words)

	An exact and an approximation algorithm for edge coloring bipartite graphs
		An exact and an approximation algorithm for edge coloring bipartite graphs
		An edge-coloring of a graph consists of an assignment of colors to its edges so that no two edges with a common endnode have the same color.
		A k-edge-coloring is one that uses at most k colors.
	www.science.unitn.it /~rrizzi/seminars/factor (213 words)

	Randomized Distributed Edge Coloring via an Extension of the Chernoff--Hoeffding Bounds
		We present fast and simple randomized algorithms for edge coloring a graph in the synchronous distributed point-to-point model of computation.
		Our algorithms compute an edge coloring of a graph $G$ with $n$ nodes and maximum degree $\Delta$ with at most $1.6 \Delta + O(\log^{1+ \delta} n)$ colors with high probability (arbitrarily close to 1) for any fixed $\delta > 0$; they run in polylogarithmic time.
		The upper bound on the number of colors improves upon the $(2 \Delta - 1)$-coloring achievable by a simple reduction to vertex coloring.
	epubs.siam.org /sam-bin/dbq/article/25076 (277 words)

	David Eppstein - Publications
		We consider several variations of the problem of coloring the squares of a quadtree so that no two adjacent squares are colored alike.
		The number of colors used by the first two algorithms is optimal; for the third algorithm, 5 colors may sometimes be needed.
		The time bound follows from limiting our attention to maximal independent subsets that are small relative to the previously colored subset, and from bounding the number of small maximal independent subsets that can occur in any graph.
	www.ics.uci.edu /~eppstein/pubs/graph-color.html (370 words)

	edge coloring (Site not responding. Last check: 2007-11-03)
		Definition: An assignment of colors (or any distinct marks) to the edges of a graph.
		A coloring is a proper coloring if no two adjacent edges have the same color.
		Paul E. Black and Algorithms and Theory of Computation Handbook, CRC Press LLC, 1999, "edge coloring", from Dictionary of Algorithms and Data Structures, Paul E. Black, ed., NIST.
	www.nist.gov /dads/HTML/edgecoloring.html (126 words)

	Chromatic sum and minimum sum multicoloring (Site not responding. Last check: 2007-11-03)
		In the minimum sum coloring problem we have to assign a color (positive integer) to each vertex of the graph such that the sum of these integers is minimal.
		In the minimum sum multicoloring problem each vertex has a demand which tells us how many colors have to be assigned to the vertex (minimum sum coloring is the special case where every demand is 1).
		As usual, the colors have to be assigned in such a way that a color cannot appear on two neighboring vertices.
	www.cs.bme.hu /~dmarx/sum.html (448 words)

Try your search on: Qwika (all wikis)