Results 31 to 40 of about 14,237 (338)
Sufficient Conditions of 6-Cycles Make Planar Graphs DP-4-Colorable
Mathematics, 2022 In simple graphs, DP-coloring is a generalization of list coloring and thus many results of DP-coloring generalize those of list coloring. Xu and Wu proved that every planar graph without 5-cycles adjacent simultaneously to 3-cycles and 4-cycles is 4 ...
Kittikorn Nakprasit +2 more
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On List Equitable Total Colorings of the Generalized Theta Graph
Discussiones Mathematicae Graph Theory, 2021 In 2003, Kostochka, Pelsmajer, and West introduced a list analogue of equitable coloring called equitable choosability. A k-assignment, L, for a graph G assigns a list, L(v), of k available colors to each v ∈ V (G), and an equitable L-coloring of G is a ...
Mudrock Jeffrey A. +2 more
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Planar graphs with $\Delta \geq 7$ and no triangle adjacent to a $C_4$ are minimally edge and total choosable [PDF]
Discrete Mathematics & Theoretical Computer Science, 2016 For planar graphs, we consider the problems of list edge coloring and list total coloring. Edge coloring is the problem of coloring the edges while ensuring that two edges that are adjacent receive different colors.
Marthe Bonamy +2 more
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The structure and the list 3-dynamic coloring of outer-1-planar graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2021 An outer-1-planar graph is a graph admitting a drawing in the plane so that all vertices appear in the outer region of the drawing and every edge crosses at most one other edge.
Yan Li, Xin Zhang
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Kempe Equivalent List Colorings
Combinatorica, 2023 29 pages, 12 figures; second version extends the main result to cliques, which were previously excluded; third version incorporates reviewer feedback; to appear in ...
Daniel W. Cranston, Reem Mahmoud
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Criticality, the list color function, and list coloring the cartesian product of graphs [PDF]
Journal of Combinatorics, 2021 We introduce a notion of color-criticality in the context of chromatic-choosability. We define a graph $G$ to be strong $k$-chromatic-choosable if $χ(G) = k$ and every $(k-1)$-assignment for which $G$ is not list-colorable has the property that the lists are the same for all vertices.
Kaul, Hemanshu, Mudrock, Jeffrey A.
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Total Equitable List Coloring [PDF]
Graphs and Combinatorics, 2018 An equitable coloring is a proper coloring of a graph such that the sizes of the color classes differ by at most one. A graph $G$ is equitably $k$-colorable if there exists an equitable coloring of $G$ which uses $k$ colors, each one appearing on either $\lfloor |V(G)|/k \rfloor$ or $\lceil |V(G)|/k \rceil$ vertices of $G$. In 1994, Fu conjectured that
Hemanshu Kaul +2 more
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On the list color function threshold
Journal of Graph Theory, 2023 AbstractThe chromatic polynomial of a graph , denoted , is equal to the number of proper ‐colorings of . The list color function of graph , denoted , is a list analogue of the chromatic polynomial that has been studied since the early 1990s, primarily through comparisons with the corresponding chromatic polynomial. It is known that for any graph there
Hemanshu Kaul +5 more
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On a List Coloring Conjecture of Reed
Journal of Graph Theory, 2002 We construct graphs with lists of available colors for each vertex, such that the size of every list exceeds the maximum vertex-color degree, but there exists no proper coloring from the lists.
Tom Bohman, Ron Holzman
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Between coloring and list-coloring: μ-coloring
Electronic Notes in Discrete Mathematics, 2005 A new variation of the coloring problem, μ-coloring, is defined in this paper. A coloring of a graph G = (V,E) is a function f : V → N such that f(v) 6= f(w) if v is adjacent to w. Given a graph G = (V,E) and a function μ : V → N, G is μ-colorable if it admits a coloring f with f(v) ≤ μ(v) for each v ∈ V .
Flavia Bonomo, Mariano Cecowski Palacio
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