Results 21 to 30 of about 115,985 (312)
Discussiones Mathematicae Graph Theory, 2023 DP-coloring is generalized via relaxed coloring and variable degeneracy in [P. Sittitrai and K. Nakprasit, Su cient conditions on planar graphs to have a relaxed DP-3-coloring, Graphs Combin. 35 (2019) 837–845], [K.M. Nakprasit and K.
Sribunhung Sarawute +3 more
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A Grover Search-Based Algorithm for the List Coloring Problem
IEEE Transactions on Quantum Engineering, 2022 Graph coloring is a computationally difficult problem, and currently the best known classical algorithm for $k$-coloring of graphs on $n$ vertices has runtimes $\Omega (2^n)$ for $k\geq 5$.
Sayan Mukherjee
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The List Edge Coloring and List Total Coloring of Planar Graphs with Maximum Degree at Least 7
Discussiones Mathematicae Graph Theory, 2020 A graph G is edge k-choosable (respectively, total k-choosable) if, whenever we are given a list L(x) of colors with |L(x)| = k for each x ∈ E(G) (x ∈ E(G) ∪ V (G)), we can choose a color from L(x) for each element x such that no two adjacent (or ...
Sun Lin +3 more
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Linear choosability of graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 A proper vertex coloring of a non oriented graph $G=(V,E)$ is linear if the graph induced by the vertices of two color classes is a forest of paths. A graph $G$ is $L$-list colorable if for a given list assignment $L=\{L(v): v∈V\}$, there exists a proper
Louis Esperet +2 more
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A Note on the Equitable Choosability of Complete Bipartite Graphs
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. +4 more
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Linear List Coloring of Some Sparse Graphs
Discussiones Mathematicae Graph Theory, 2021 A linear k-coloring of a graph is a proper k-coloring of the graph such that any subgraph induced by the vertices of any pair of color classes is a union of vertex-disjoint paths. A graph G is linearly L-colorable if there is a linear coloring c of G for
Chen Ming, Li Yusheng, Zhang Li
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AKCE International Journal of Graphs and Combinatorics, 2023 We introduce a concept in graph coloring motivated by the popular Sudoku puzzle. Let [Formula: see text] be a graph of order n with chromatic number [Formula: see text] and let [Formula: see text] Let [Formula: see text] be a k-coloring of the induced ...
J. Maria Jeyaseeli +3 more
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On DP-Coloring of Digraphs [PDF]
, 2018 DP-coloring is a relatively new coloring concept by Dvo\v{r}\'ak and Postle and was introduced as an extension of list-colorings of (undirected) graphs.
Bang-Jensen, Jørgen +3 more
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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 $ (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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The list Distinguishing Number Equals the Distinguishing Number for Interval Graphs
Discussiones Mathematicae Graph Theory, 2017 A distinguishing coloring of a graph G is a coloring of the vertices so that every nontrivial automorphism of G maps some vertex to a vertex with a different color. The distinguishing number of G is the minimum k such that G has a distinguishing coloring
Immel Poppy, Wenger Paul S.
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