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Tree-Chromatic Number Is Not Equal to Path-Chromatic Number [PDF]
Journal of Graph Theory, 2017 For a graph G and a tree-decomposition (T,B) of G, the chromatic number of (T,B) is the maximum of χ(G[B]), taken over all bags B∈B. The tree-chromatic number of G is the minimum chromatic number of all tree-decompositions (T,B) of G.
Kim, Ringi, Huynh, Tony
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Local chromatic number and topology [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 The local chromatic number of a graph, introduced by Erdős et al., is the minimum number of colors that must appear in the closed neighborhood of some vertex in any proper coloring of the graph.
Gábor Simonyi, Gábor Tardos
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0034 | Chromatic Number and Neutrosophic Chromatic Number
, 2021 New setting is introduced to study chromatic number. Neutrosophic chromatic number and chromatic number are proposed in this way, some results are obtained.
Henry Garrett
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DICHROMATIC NUMBER AND FRACTIONAL CHROMATIC NUMBER
Forum of Mathematics, Sigma, 2016 The dichromatic number of a graph $G$ is the maximum integer $k$
BOJAN MOHAR, HEHUI WU
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Journal of Combinatorial Theory, Series B, 2015 Let us say a graph G has “tree-chromatic number” at most k if it admits a tree-decomposition (T, (X-t : t is an element of V (T))) such that G[X-t] has chromatic number at most k for each t is an element of V (T). This seems to be a new concept, and this
Seymour, Paul D.
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On circulant chromatic number and circulant chromatic function
Discrete Mathematics, 2001 A new concept of circulant chromatic function of a graph is introduced to generalize the concept of chromatic polynomial of a graph. This is similar to the generalization from the concept of chromatic number to the concept of circulant chromatic number ...
Zhixiong Wang +3 more
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The b-chromatic number of power graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2003 The b-chromatic number of a graph G is defined as the maximum number k of colors that can be used to color the vertices of G, such that we obtain a proper coloring and each color i, with 1 ≤ i≤ k, has at least one representant x i adjacent to a
Brice Effantin, Hamamache Kheddouci
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Monotone Chromatic Number of Graphs
International Journal of Analysis and Applications, 2020 For a graph G = (V, E), a vertex coloring (or, simply, a coloring) of G is a function C: V (G) → {1, 2, ..., k} (using the non-negative integers {1, 2, ..., k} as colors).
Anwar Saleh +3 more
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Chromatic number via Turán number
Discrete Mathematics, 2017 For a graph G and a family of graphs F, the general Kneser graph KG(G, F) is a graph with the vertex set consisting of all subgraphs of G isomorphic to some member of F and two vertices are adjacent if their corresponding subgraphs are edge disjoint.
Alishahi, Meysam +3 more
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Discrete Mathematics, 1994 The mean chromatic number of a graph is a measure of the expected performance of the greedy vertex-colouring algorithm when each ordering of the vertices is equally likely.
Anthony, Martin
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