Results 51 to 60 of about 2,394 (219)
Expansions of the chromatic polynomial
Discrete Mathematics, 1973 AbstractThe chromatic polynomial (or chromial) of a graph was first defined by Birkhoff in 1912, and gives the number of ways of properly colouring the vertices of the graph with any number of colours. A good survey of the basic facts about these polynomials may be found in the article by Read [3].It has recently been noticed that some classical ...
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Some inequalities for the Tutte polynomial
, 2011 This is the post-print version of the Article. The official published version can be accessed from the link below - Copyright @ 2011 ElsevierWe prove that the Tutte polynomial of a coloopless paving matroid is convex along the portion of the line x+y=p ...
Noble, Steven D. +15 more
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The chromatic sum of a graph: history and recent developments
International Journal of Mathematics and Mathematical Sciences, 2004 The chromatic sum of a graph is the smallest sum of colors among all proper colorings with natural numbers. The strength of a graph is the minimum number of colors necessary to obtain its chromatic sum.
Ewa Kubicka
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An inequality for chromatic polynomials
Discrete Mathematics, 1992 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Signed Projective Cubes, a Homomorphism Point of View
Journal of Graph Theory, EarlyView.ABSTRACT The (signed) projective cubes, as a special class of graphs closely related to the hypercubes, are on the crossroad of geometry, algebra, discrete mathematics and linear algebra. Defined as Cayley graphs on binary groups, they represent basic linear dependencies.
Meirun Chen +2 more
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Cubical coloring — fractional covering by cuts and semidefinite programming [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 We introduce a new graph parameter that measures fractional covering of a graph by cuts. Besides being interesting in its own right, it is useful for study of homomorphisms and tension-continuous mappings.
Robert Šámal
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Properties of chromatic polynomials of hypergraphs not held for chromatic polynomials of graphs
European Journal of Combinatorics, 2017 3 figures, 22 pages, 48 references.
Ruixue Zhang, Fengming Dong
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Orientations of Graphs With at Most One Directed Path Between Every Pair of Vertices
Journal of Graph Theory, EarlyView.ABSTRACT Given a graph G $G$, we say that an orientation D $D$ of G $G$ is a KT orientation if, for all u , v ∈ V ( D ) $u,v\in V(D)$, there is at most one directed path (in any direction) between u $u$ and v $v$. Graphs that admit such orientations have been used to construct graphs with large chromatic number and small clique number that served as ...
Barbora Dohnalová +3 more
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Coefficients of chromatic polynomials and tension polynomials
Contributions to Discrete Mathematics, 2011 We evaluate coefficients of chromatic polynomial of a graph G as sums of zero values of tension polynomials of certain "maximal" subgraphs of G.
Martin Kochol, Nad'a Krivonáková
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Journal of Graph Theory, EarlyView.ABSTRACT In an effort to understand the complexity of the maximum independent set problem, Chvátal introduced t‐perfect graphs. While a full characterization of this class remains open, important progress has been made for claw‐free graphs [Bruhn and Stein, Math. Program. 2012] and P 5 ${P}_{5}$‐free graphs [Bruhn and Fuchs, SIAM J. Discrete Math. 2017]
Yixin Cao, Shenghua Wang
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