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Topic: Uniquely colorable graph

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	Graph coloring - Wikipedia, the free encyclopedia
		In graph theory, graph coloring is an assignment of "colors", almost always taken to be consecutive integers starting from 1 without loss of generality, to certain objects in a graph.
		Graph coloring is not to be confused with graph labeling, which is an assignment of labels, usually also in the form of numbers, to vertices or edges.
		The problem of coloring a graph has found a number of applications such as scheduling, register allocation in compilers, frequency assignment in mobile radios, and pattern matching.
	en.wikipedia.org /wiki/Graph_coloring (1104 words)

	Uniquely colorable graph - Wikipedia, the free encyclopedia
		In graph theory, a uniquely colorable graph is a k-chromatic graph that has only one possible (proper) k-coloring up to permutation of the colors.
		A uniquely total colorable graph is a k-total-chromatic graph that has only one possible (proper) k-total-coloring up to permutation of the colors.
		Empty graphs, paths, and cycles of length divisible by 3 are uniquely total colorable graphs.
	en.wikipedia.org /wiki/Uniquely_colorable_graph (294 words)

	Graph coloring
		The problem of coloring a graph has found a number of applications such as scheduling, register allocation in a microprocessor, frequency assignment in mobile radios, and pattern matching.
		The chromatic polynomial of a graph was introduced by Birkhoff and Lewis in their attack on the four-color theorem.
		It remains an unsolved problem to charecterize graphs which have the same chromatic polynomial and to determine precisely what polynomials are chromatic.
	www.mcfly.org /wik/Graph_coloring (1001 words)

	Unique prime - Encyclopedia Glossary Meaning Explanation Unique prime (Site not responding. Last check: 2007-10-09)
		In mathematics, a unique prime is a certain kind of prime number.
		A prime p ≠ 2, 5 is called unique iff there is no other prime q such that the period length of the decimal expansion of its reciprocal, 1 / p, is equivalent to the period length of the reciprocal of q, 1 / q.
		Unique primes were first described by Samuel Yates in 1980.
	www.encyclopedia-glossary.com /en/Unique-prime.html (199 words)

	Week 3 Abstracts
		The choice number ch(G) of a graph G is the minimum integer k such that for every assignment of a list S(v) of k colors to every vertex v of G (lists for different vertices may be different), there is a proper coloring of G that assigns to each vertex v a color from S(v).
		We prove that every graph on the Klein Bottle which does not contain contractible cycles of length 3 or 4 is either 3-colorable or has a subgraph isomorphic to a member of a particular family of non-3-colorable graphs.
		The Kneser graph K(n,k) is the graph of the disjointness relation on the k-element subsets of an n-set.
	dimacs.rutgers.edu /drei/1998/week3.html (3950 words)

	The Four Color Theorem
		The coloring of geographical maps is essentially a topological problem, in the sense that it depends only on the connectivities between the countries, not on their specific shapes, sizes, or positions.
		The graph of a set of three mutually adjoining regions is simply a topological triangle, and if we add a fourth region, it is represented by a fourth vertex in the graph, which must be located either inside or outside the triangle formed by the graph of the original three vertices.
		In this context the four color theorem tells us that a space of four dimensions is sufficient to enable us to assign one of the four basis vectors to each vertex of a planar graph in such a way that the vectors of every pair of adjacent vertices are orthogonal.
	www.mathpages.com /home/kmath266/kmath266.htm (4081 words)

	Micro biography of (Site not responding. Last check: 2007-10-09)
		The collaboration graph of mathematicians and a conjecture of Erdos.
		An exposition of the reconstruction conjecture for graphs.
		(R.A. Melter) On the metric dimension of a graph.
	www.cs.nmsu.edu /~fnh/publ.html (3284 words)

	Phase Transition in Graph Coloring, Frozen Development and Data Files (Site not responding. Last check: 2007-10-09)
		It then builds a sequence of graphs starting with the empty graph and finishing with a 3-partite complete graph, where each graph in the sequence differs from the previous one by the addition of the next edge, except for those edges which are previously frozen with respect to three colorings.
		That is, for some earlier graph in the sequence all legal 3-colorings required this pair to have different colors, and this property holds for all following graphs in the sequence.
		In this case, the frozen index indicates the earliest graph in the sequence for which this property holds; that is, it is the label of the pair that caused pair i to become freely addable.
	www.cs.ualberta.ca /~joe/Coloring/Frozen/fzdv.html (792 words)

	Some Concepts in List Coloring - Eslahchi, Ghebleh, Hajiabolhassan (ResearchIndex) (Site not responding. Last check: 2007-10-09)
		A graph G is said to be uniquely k--list colorable if it admits a k--list assignment from which G has a unique list coloring.
		The minimum k for which G is not uniquely k--list colorable is called the m--number of G. We show that every triangle--free uniquely colorable graph with chromatic number k + 1 is uniquely k--list colorable.
		A bound for the m--number of graphs is given, and using this bound it is shown that every planar...
	citeseer.ist.psu.edu /687788.html (526 words)

	chap-7
		Observe that if a connected graph has chromatic number equal to two, then all of these colorings are equivalent, in the sense that the partitions of the vertices they induce are all the same.
		We could find the valid colorings of a graph by traversing each of its search tree paths completely, not testing the validity of the corresponding coloring until the end of the path was reached.
		If we invert the colors in H2(1,3), changing every color-1 to color-3, and color-3 to color-1 and leave the colors in H1(1,3) unchanged, we obtain a valid coloring in which v1 and v3 are both color-1; so we are free to color v with 3.
	www.cis.njit.edu /~mchugh/psswrd/web-course-materials/graph-theory/alg-graph-theory-text-html/chap-7-text-v2.html (4854 words)

	Uniquely colorable graph - Encyclopedia Glossary Meaning Explanation Uniquely colorable graph (Site not responding. Last check: 2007-10-09)
		Uniquely colorable graph - Encyclopedia Glossary Meaning Explanation Uniquely colorable graph.
		Here you will find more informations about Uniquely colorable graph.
		The orginal Uniquely colorable graph article can be editet
	www.encyclopedia-glossary.com /en/Uniquely-colorable-graph.html (358 words)

	37a (Site not responding. Last check: 2007-10-09)
		Uniquely colorable perfect graphs (in which there is a unique partition into
		There is also a combinatorial good characterization theorem for unique colorability of perfect graphs, and a polynomial algorithm for testing the property using the ellipsoid method (IPCO 1, Kannan, Pulleyblank eds, Waterloo Univ. Press, 1990).
		It can be simply proved that a minimal imperfect graph with three forced vertices in particular positions is an odd hole or an odd antihole.
	www.aimath.org /WWN/perfectgraph/articles/html/37a (235 words)

	[No title] (Site not responding. Last check: 2007-10-09)
		Note that for $c$ small enough the graph almost surely has maximum degree less than 3, and os is easily colorable.
		Note the graph coloring is a special case.}) @article(hogg96,author= {Tadd Hogg},title= {Refining the phase transition in combinatorial search},journal= ai,year= 1996,volume= 81,number= {1--2},pages= {127--154},annote= {Tests transition on clustered grapsh using bst ultrametric, connected graphs and padded graphs where in every vertex has at least min degree.
		It points out that {\em CWMAX is} an upper bound on the chromatic number.}) @incollection(kor79,author= {Samuel M. Korman},title= {The Graph-Colouring Problem},booktitle= {Combinatorial Optimization},publisher= wiley,address= {New York},year= 1979,editor= {Nicos Christofides and Aristide Mingozzi and Paolo Toth and Claudio Sandi},pages= {211--235},keywords= {graph color exact algorithms}) @article(kor80,author= {A. Korshunov},title= {The Chromatic Number of $n$-Vertex Graphs},journal= {Diskret.
	www.cs.ualberta.ca /~joe/Coloring/Bibliography/color.bib (473 words)

	Colorable
		While the court agreed with Empire?Äôs general views on possible environmental liability, it found that "the mere assertion of a colorable claim by the contractor (later found to be meritless) that...
		These marks, and any colorable imitation of such, may not be used in any manner or for any purpose without the prior written consent of ALPINE.
		And there is that sweet colorable suppression issue that popped right out in a client interview this morning that I'll get to work on (car passenger, driver's arrested on a warrant, no warrants on my...
	freeprintablecoloringpages.scadprintable.com /colorable (925 words)

	Discrete Mathematics. (Site not responding. Last check: 2007-10-09)
		Era, M. Tsuchiya, On upper bound graphs whose complements are also upper bound graphs, Discrete Mathematics 179 (1-3) (1998) pp.
		Toma Pisanski, Thomas W. Tucker, Boris Zgrabli, Strongly adjacency-transitive graphs and uniquely shift-transitive graphs, Discrete Mathematics 244 (1-3) (2002) pp.
		Hajiabolhassan, M.L. Mehrabadi, R. Tusserkani, Minimal coloring and strength of graphs, Discrete Mathematics 215 (1-3) (2000) pp.
	www.elsevier.com /cdweb/journals/0012365X/viewer.htt?viewtype=authors&rangeselected=162 (725 words)

	Graph coloring (Site not responding. Last check: 2007-10-09)
		The corresponding decision problem (is there a coloring which uses at most
		colors?) is NP-complete, and in fact was one of Karp's 21 NP-complete problems.
		fractional coloring - vertices may have multiple colors, and on each edge the sum of the color parts of each vertex is not greater than one Some improper colorings:
	www.worldhistory.com /wiki/G/Graph-coloring.htm (1160 words)

	Vitaly Voloshin: Basic concepts on mixed hypergraph coloring (Site not responding. Last check: 2007-10-09)
		In a coloring of mixed hypergraph, a subset Y⊆X is
		In a colorable mixed hypergraph H, the maximum (minimum) number of colors over all strict k-colorings is called the
		This means that in every coloring, bi-edge is neither monochromatic nor polychromatic subset of vertices.
	math.net.md /voloshin/basic.html (561 words)

	Joint Meetings of the Iowa MAA, ASA, and IMATYC (Site not responding. Last check: 2007-10-09)
		Suppose that P is a subset of the vertices of a graph G with chromatic number r, where P induces a set of k-cliques and all of the vertices of P are precolored.
		There exists a finite critical distance so that for any graph, if the k-cliques are at least this distance apart, then any (r+1)-coloring of P will extend to an (r+1)-coloring of G. In this talk, I will describe several results found while looking for such a critical distances for planar graphs.
		I give an example of a planar graph in which a certain precoloring of P does not extend to a coloring of G. This example gives a lower bound for a critical distance.
	maa-ia.cornell-iowa.edu /SpringNews2000/Abstracts.htm (1713 words)

	[No title]
		Graph A is homeomorphic to graph B, if by a sequence of edge deletions and coalescence of vertices, graph B can be obtained from graph A. Isomorphism of graphs is an equivalence relation, but homeomorphism in this sense is not.
		For instance, if we use the whole set of integers and select the ones generated by f(n) = 2n, every function of the form g(n) = 2n - (2m + 1) is going to be a complement to f(n) for all integers m.
		Either you already know a generating function, or you'll be hard pressed to find one, since you'll have to know all terms of the sequence without knowing a generating function to give them to you.
	www.grahamkendall.net /Math/MathNewsgroups/mm-366.txt (20824 words)

	Problems in Topological Graph Theory
		Graphs that quadrangulate both the torus and Klein bottle
		Orientable genus of graphs of bounded nonorientable genus
		Interpolation conjectures on separating cycles in embedded graphs
	www.emba.uvm.edu /~archdeac/problems/problems.html (283 words)

	Publications
		B) The lattice-graph of the topology of a transitive directed graph.
		Triangles in line-graphs and total graphs (with M. Behzad and E. Nordhaus) Indian J. Math.
		The cube of every connected graph is 1-hamiltonian.
	homepages.wmich.edu /~zhang/g65.html (113 words)

	Anthony Bonato's Homepage
		Spanning subgraphs of graphs partitioned into two isomorphic pieces; pdf, accepted in the Journal of Graph Theory.
		A note on orientations of the infinite random graph, with D.
		Skolem arrays and Skolem labellings of ladder graphs, with C.
	info.wlu.ca /~wwwmath/faculty/bonato/papers.html (404 words)

	UIUC CS491 Theory Fall '98 (Site not responding. Last check: 2007-10-09)
		We show that the chip problem is closely related to a modified majority problem in the worst case and use this fact to obtain upper and lower bounds on algorithms for the chip problem.
		It is therefore of some interest to determine which error-correcting codes correspond to a cycle-free Tanner graph representation; this problem can also be stripped of its coding-theory basis and considered as a problem in graph theory.
		The largest [smallest] number of colors for which there exists a coloring using that many colors is called the upper [lower] chromatic number of $H$, denoted by $\bar{\chi }(H)$ [$\chi (H)$].
	compgeom.cs.uiuc.edu /~feidazhu/cs491f98.html (2082 words)

	Generalizations of The Four Color Theorem (Site not responding. Last check: 2007-10-09)
		This is not a comprehensive survey, but rather a short pointer to as-yet unpublished results that people often ask about.
		Every 2-connected 3-regular graph with no minor isomorphic to the Petersen graph is edge 3-colorable.
		A 3-regular planar graph has a unique edge 3-coloring if and only it can be obtained from the complete graph on four vertices by repeatedly replacing vertices by triangles.
	www.math.gatech.edu /~thomas/FC/generalize.html (159 words)

	Jeff Dinitz
		Orthogonal edge colorings of graphs (with D.S. Archdeacon and F. Harary), Congressus Numerantium 47 (1985) pp.
		The irregularity strength of the m x n grid (with D. Garnick and A. Gyarfas), Journal of Graph Theory 16 (1992), pp.
		The stipulation polynomial of a uniquely list-colorable graph (with W.J. Martin), Australasian Journal of Combinatorics, 11 (1995), pp.
	www.emba.uvm.edu /~dinitz/vita.html (1795 words)

	Proceedings of the American Mathematical Society
		H. Abbott and B. Zhou, The star chromatic number of a graph, J. Graph Theory 17 (1993), 349-360.
		D. Guichard, Acyclic graph coloring and the complexity of the star chromatic number, J. Graph Theory 17 (1993), 129-134.
		X. Zhu, Graphs whose circular chromatic number equals the chromatic number, Combinatorica, 19(1)(1999), 139-149.
	www.ams.org /proc/2001-129-10/S0002-9939-01-05908-1/home.html (344 words)

	Forcing Structures and Cliques in Uniquely Vertex Colorable Graphs
		Forcing Structures and Cliques in Uniquely Vertex Colorable Graphs: SIAM Journal on Discrete Mathematics Vol.
		Let G be a simple undirected uniquely vertex k-colorable graph, or a k-UCG for short.
		Truszczyandnacute;ski [Some results on uniquely colorable graphs, in Finite and Infinite Sets, North-Holland, Amsterdam, 1984, pp.
	epubs.siam.org /sam-bin/dbq/article/30499 (248 words)

	Greenwell's Resume (Site not responding. Last check: 2007-10-09)
		M.S. in Mathematics, Vanderbilt University, 1968, On Reconstructing Graphs.
		Ph.D. in Mathematics, Vanderbilt University, 1973, Graphs With Forbidden Subgraphs.
		"Reconstructing the n-connected components of a graph", (with R. Hemminger), Aequationes Mathematicae, 9(l973), pp.
	www.math.eku.edu /Greenwell/vita.html (1426 words)

	K r -free Uniquely Vertex Colorable Graphs (ResearchIndex) (Site not responding. Last check: 2007-10-09)
		These families of graphs are indeed counter examples to Shaoji's Conjecture.
		3 Uniquely colorable graphs (context) - Harary, Hedetniemi et al.
		1 On uniquely 3-colorable graphs (context) - Chao, Chen - 1993 ACM
	citeseer.ist.psu.edu /573624.html (176 words)

	Discrete Applied Mathematics. (Site not responding. Last check: 2007-10-09)
		Rowlinson, The characteristic polynomials of modified graphs, Discrete Applied Mathematics 67 (1-3) (1996) pp.
		Davies, G.F. Royle, Graph domination, tabu search and the football pool problem, Discrete Applied Mathematics 74 (3) (1997) pp.
		Ruskey, M. Jiang, A. Weston, The Hamiltonicity of directed sigma-tau Cayley graphs (Or: A tale of backtracking), Discrete Applied Mathematics 57 (1) (1995) pp.
	www.elsevier.com /cdweb/journals/0166218X/viewer.htt?viewtype=authors&rangeselected=74 (452 words)

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