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Topic: Snark (graph theory)

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	Snark (graph theory) - Wikipedia, the free encyclopedia
		The flower snark is one of 6 snarks on 20 vertices.
		In graph theory, a snark is a connected, bridgeless cubic graph with chromatic index equal to 4.
		Tait initiated the study of snarks in 1880, when he proved that the four color theorem is equivalent to the statement that no snark is planar.
	en.wikipedia.org /wiki/Snark_(graph_theory) (272 words)

	Kids.Net.Au - Encyclopedia > The Hunting of the Snark
		Lewis Carroll's The Hunting of the Snark (An Agony in 8 Fits) is a comic poem about a group of adventurers hunting a legendary beast.
		The Baker recalls that his uncle once warned him that, though catching Snarks was all well and good, you must be careful; for, if your Snark is a Boojum, then "you will softly and silently vanish away, and never be met with again." With this in mind, they split up to hunt.
		The word "snark" has since been used in graph theory, as has "boojum", and was also used, chillingly aptly, as the name of the SM-62 Snark[?] nuclear cruise missile.
	www.kids.net.au /encyclopedia-wiki/th/The_Hunting_of_the_Snark (474 words)

	Wikipedia: Snark
		They are warned that if their snark is a boojum they will swiftly and silently vanish away and never be heard of again.
		The word "snark" is an amalgam of "snake" and "shark".
		The SM-62 Snark was an intercontinental nuclear cruise missile of the US Air Force that was operational in 1960 and 1961.
	www.factbook.org /wikipedia/en/s/sn/snark.html (218 words)

	The eponymous snark in Lewis Carroll Lewis Carroll s The Hunting...
		The eponymous "snark" in Lewis Carroll Lewis Carroll's "The Hunting of the Snark The Hunting of the Snark" is a fictional animal, the quarry for a hunting party comprising some highly unlikely characters.
		In graph theory graph theory, a "snark" is a graph graph in which each vertex vertex has three edge edges, but it is impossible to color the edges with only three colors so that edges of the same color don't meet at one vertex.
		The SM-62 Snark SM-62 Snark was an intercontinental nuclear cruise missile cruise missile of the US Air Force US Air Force that was operational in 1960 1960 and 1961 1961.
	www.biodatabase.de /Snark (473 words)

	PlanetMath: Vizing's theorem
		Only in the context of graph colorings is Shannon's theorem understood to refer to the one here; in the wider world the term tends to refer to any of his fundamental theorems in information theory.
		A(n edge-)critical graph is a connected graph of class II but such that removing any of its edges makes it class I. As often in graph theory, such a minimality condition imposes a certain amount of structure on the graph.
		The Petersen graph is one, and a few infinite families of snarks have been found.
	planetmath.org /encyclopedia/EdgeChromaticNumber.html (813 words)

	School of Mathematics and Statistics - Graph Theory at UNSW - Past and Present
		Graphs are very useful for modelling the relationships which exist between objects in a network or system.
		Snarks are very special graphs with most known examples exhibiting a lot of symmetry, whereas random graphs rarely display any symmetry at all.
		One use of random graphs is to provide "average case" analysis for researchers, such as physicists or computer scientists, who use graphs to model a system of interest.
	www.maths.unsw.edu.au /school/articles/unswgraphtheory.html (1596 words)

	Snarks
		A snark (graph theory) is a graph in which each vertex has three edges, but it is impossible to color the edges with only three colors so that edges of the same color do not meet at one vertex.
		A Websnark snark is not necessarily snide; it derives from the website's name, which in turn derives from snark (speech).
		"Snark" is a tradename for an early single-hose diving regulator.
	www.sfcrowsnest.com /scifinder/a/Snark.php (621 words)

	Encyclopedia Search
		The group is led by a Bellman Bellman Bellman, and consists otherwise...
		is a graph in which each vertex has three...
		has since been used in graph theory, as has boojum, and was also used,...
	www.encyclopedian.com /search.php?searWords=Snark (154 words)

	Atlas: Construction of Irreducible and Critical Snarks with High Cyclical Connectivity by E. Ricanyova (Site not responding. Last check: 2007-11-05)
		A snark is nontrivial cubic graph whose edges cannot be properly coloured by three colours.
		Roughly speaking, a snark G is irreducible if there is no possibility of replacing an induced subgraph of G by anything smaller so that the resulting graph remains cubic and uncolorable.
		A snark is said to be strongly irreducible if the removal of any two non-adjacent edges gives rise to a colourable graph, and a snark is said to be critical if removing any two adjacent vertices produces a colourable graph.
	atlas-conferences.com /c/a/f/d/21.htm (463 words)

	Snark (graph theory) - Wikipedia, the free encyclopedia
		In graph theory, a snark is a connected, bridgeless cubic graph with chromatic index equal to four.
		The well-known four color theorem is equivalent to the statement that no snark is planar.
		The four flow conjecture of Bill Tutte in the case of cubic graphs states that every snark contains the Petersen graph as a minor.
	www.godseye.com /stat/en/s/n/a/Snark_(graph_theory).html (183 words)

	Graph Theory Glossary - s-so (Site not responding. Last check: 2007-11-05)
		A vertex in a graph which is on an edge of a matching is said to be saturated.
		A graph that is not connected or has at least one cut vertex; equivalently, a graph of connectivity at most 1.
		In a graph or network, this is a path from one node to another whose total cost is the least among all such paths.
	www.cc.ioc.ee /jus/gtglossary/gtglos_s_so.htm (2396 words)

	Hunting of the Snark, The :: Titles
		Snark (Lewis Carroll), a fictional animal in Lewis Carroll's The Hunting of the Snark
		Snark (speech), a style of speech/writing that could loosely be described as "snidely derisive"
		Snark (diving regulator), a tradename for an early single-hose diving regulator
	arts.gourt.com /Animation/Movies/Titles/Hunting-of-the-Snark,-The.html (173 words)

	AMCA: Critical and Bicritical Snarks of Cyclic Connectivity 4 by M. Chladny (Site not responding. Last check: 2007-11-05)
		A snark is a ``non-trivial'' cubic graph with edge chromatic number 4.
		This is because a snark deviating from this girth-and-connectivity condition can be obtained from a smaller snark or two smaller snarks in a trivial manner.
		Bicritical snarks are in fact k-irreducible for all k and therefore they are of special interest as ``the most non-trivial'' of all snarks.
	at.yorku.ca /c/a/f/d/05.htm (504 words)

	Examples 15 (Site not responding. Last check: 2007-11-05)
		A snark is a non-trivial cubic graph whose edges cannot be properly coloured by three colours.
		Primarily it means a graph without a bridge, but it can also include (and in some cases not) some other properties, like that a non-trivial snark should have girth 5 or more.
		In package Vega there are four different snarks: Blanusa1, which constructs a Blanusa snark B1, then DoubleStarSnark, which returns a generalized double star snark Ds, then there is FlowerSnark, giving the family of flower snarks In, and at last GoldbergSnark, returning the generalized Goldberg snark GL.
	vega.ijp.si /HtmlDoc/MANUAL/EXMPLS15.HTM (287 words)

	Spring 2004: Graphs and Combinatorial Invariants
		This course is an introduction to some advanced aspects of graph theory and to Tutte invariants of graphs and matroids.
		The focus of the course is on some contributions of Tutte, arguably the greatest graph theorist of the last century (neglecting Robertson and Seymour as transcenturial), and work that follows in his spirit.
		A "snark" is defined to exclude graphs with a bond of 2 or 3 edges, because their snarkiness is derived from that of a residual graph, H
	www.math.binghamton.edu /zaslav/Oldcourses/580.S04 (2227 words)

	Research Interests (Site not responding. Last check: 2007-11-05)
		Not having a course specifically in graph theory at my undergraduate university (Clarkson), Christino Tamon and I had a directed study of graph theory and I made it the topic area of my honors undergraduate thesis.
		Rigorous proofs, novel algorithm development and theoretical analysis are important aspects of graph theory research, but should not always be the final end.
		The analysis of social networks is an area where the rich field of graph theory may be applied to practical problems.
	www.cs.rpi.edu /~baumej/ResearchInterests.xml (333 words)

	Discrete Structures - Math 447 - TR 2:00-3:15 <br> Syllabus Fall 2000
		A combinatorial graph G = (V,E) is a set of vertices V and edges E, each edge consisting of unordered pairs of vertices.
		We picture graphs with dots for vertices in any desired arrangement and lines for edges, connected pairs of vertices in that edge.
		For example, the electrical engineer will be interested in planar graphs and the computer scientist in algorithms to properly color graphs.
	www.math.uri.edu /~eaton/mth447f00.html (842 words)

	Mary Stella's Postcards from Paradise - Bravenet Blog
		Snarking seems to be the discussion style du jour.
		When someone has a snark fest going on a blog, I find that whatever valid points might exist are lost in the tone of the words.
		I don't succumb to the dark side of the snark snicker I made it mean this, and to me it still does..
	starfabu.bravejournal.com /entry/13780 (939 words)

	Blanusa's snark, Danilo Blanusa, W.T. Tutte, Blanche Descartes (Site not responding. Last check: 2007-11-05)
		Beside this idea he has offered and depicted graph showning that the Petersen graph is not the only one of this type.
		Step by step further discoveries led to the branch of Graph Theory called Theory of Snarks.
		The term "snark" owes its origins to the Snark of Lewis Carroll fame ("The hunting of the Snark").
	www.hr /darko/etf/ivansic.html (266 words)

	Blanusa Snarks -- from Wolfram MathWorld
		The first and second Blanusa snarks (several embeddings of which are illustrated in the top and bottom rows above, respectively), were the second and third
		Alas, I did not understand the language, but the diagram made all clear!" The Blanusa snarks each have 18 vertices and edge chromatic number 4.
		The Blanusa snarks are used as the logo for the Croatian Mathematical Society (Ivansic).
	mathworld.wolfram.com /BlanusaSnarks.html (200 words)

	Mathematica Slovaca (Site not responding. Last check: 2007-11-05)
		Bicritical snarks are the irreducible ones with respect to the reductions considered by Nedela and \v{S}koviera in [NEDELA,~R.---\v{S}KOVIERA,M.: {\it Decompositions and reductions of snarks\/}, J.~Graph Theory {\bf 22} (1996), 253--279.
		We show that for some $n \geq 10$ and for each even $n \geq 92$ there is a hypohamiltonian and henceforth bicritical snark of order $n$.
		This solves a problem stated in [NEDELA,~R.---\v{S}KOVIERA,M.: {\it Decompositions and reductions of snarks\/}, J.~Graph Theory {\bf 22} (1996), 253--279.
	www.mat.savba.sk /maslo/paper.php?id_paper=416 (75 words)

	Detaily diplomovej práce (Site not responding. Last check: 2007-11-05)
		The real flow number $\Phi_\mathbb{R}(G)$ of a graph $G$ is the infimum of all reals $r$ such that $G$ has a real nowhere-zero $r$-flow.
		We answer their question whether for each rational number $4snark with real flow number $r$ by constructing an infinite family of snarks for each such $r$.
		As a consequence we show that the real flow number of the Isaacs snark $I_{2k+1}$ is $\Phi_\mathbb{R}(I_{2k+1})=4+1/k$, completing the upper bound of E.
	www.dcs.fmph.uniba.sk /diplomovky/registracia/Detail.php?id=62 (231 words)

	Graph Theory Encyclopedia Article @ PSAMathe.com (PSA Mathe) (Site not responding. Last check: 2007-11-05)
		It takes ideas from other disciplines, such as graph theory, and in turn provides tools for modeling and investigating such networks [see (32) for a recent...
		More Graph Theory Page Titles on this Site
		PSAMathe.com is designed and maintained by Kurt Karr and is hosted by pair Networks.
	www.psamathe.com /encyclopedia/Category:Graph_theory (106 words)

	Curriculum Vitae - Rizzi Romeo
		Journal of Graph Theory 32 (1) (1999) 1-15.
		A main theme of LEA group in the Department of Mathematics of Trento University is the realization of ``intertools'' available under WEB for the heuristic solution of NP-complete problems.
		This is a project of the Free University of Bozen which has lead the pupils of the several primary schools of Bozen to design, project and create their journal in the web.
	www-math.science.unitn.it /~rrizzi/curricula/englishCV/englishCV.html (701 words)

	Szekeres Snark -- from Wolfram MathWorld
		Graph Theory > Simple Graphs > Noneulerian Graphs
		It has 50 vertices and edge chromatic number 4.
		Szekeres, G. "Polyhedral Decompositions of Cubic Graphs." Bull.
	mathworld.wolfram.com /SzekeresSnark.html (123 words)

	Home Page of Deniz Sarioz
		As a member of the Discrete Imaging and Graphics group, I have also had the pleasure of maintaining the Snark05 Utilities for a couple of years.
		My current research interests span algorithm analysis and design, approximation algorithms, online algorithms, "applied" complexity theory, combinatorics, geometry, graph theory, and cryptology.
		Undergraduate mathematics thesis, Isomorphism of graphs derived from voltage graphs.
	www.sarioz.com (568 words)

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