Results 21 to 30 of about 44,462 (291)
New Results on Edge-Coloring and Total-Coloring of Split Graphs [PDF]
Discrete Applied Mathematics, 2023 20 pages, 5 ...
Fernanda Couto +2 more
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Edge and total coloring of interval graphs [PDF]
Discrete Applied Mathematics, 2001 Let \(\chi_e(G)\) and \(\chi_{ve}(G)\) be the edge and total chromatic number of a graph \(G\). It is clear that \(\chi_{e}(G)\geq\Delta(G)\) and \(\chi_{ve}(G)\geq\Delta(G)+1\), where \(\Delta(G)\) is the maximum degree of \(G\). By Vizing's theorem, \(\chi_{e}(G)\leq\Delta(G)+1\) for each \(G\).
Bojarshinov, V.A.
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Total fuzzy graph coloring [PDF]
Journal of Hyperstructures, 2023 In this paper, a hybrid genetic algorithm (HGA) is proposed for the total fuzzy graph coloring (TFGC) problem. TFGC comprises of a graph with fuzzy vertices and edges, seeks to obtain an optimal $k-$coloring of that fuzzy graph such that the degree of ...
Smriti Saxena +2 more
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On total coloring and equitable total coloring of infinite snark families
RAIRO - Operations Research, 2023 We show that all members of the SemiBlowup, Blowup and the first Loupekine snark families have equitable total chromatic number equal to 4. These results provide evidence of negative answers for the questions proposed: by (A. Cavicchioli, T.E. Murgolo, B. Ruini and F. Spaggiari, Acta Appl. Math.
Miguel A. D. R. Palma +3 more
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Neighbor sum distinguishing list total coloring of IC-planar graphs without 5-cycles [PDF]
, 2022 summary:Let $G=(V(G),E(G))$ be a simple graph and $E_{G}(v)$ denote the set of edges incident with a vertex $v$. A neighbor sum distinguishing (NSD) total coloring $\phi $ of $G$ is a proper total coloring of $G$ such that $\sum _{z\in E_{G}(u)\cup \{u\}}
Zhang, Donghan
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Equitable Total Coloring of Corona of Cubic Graphs
Discussiones Mathematicae Graph Theory, 2021 The minimum number of total independent partition sets of V ∪ E of a graph G = (V, E) is called the total chromatic number of G, denoted by X′(G). If the di erence between cardinalities of any two total independent sets is at most one, then the minimum ...
Furmańczyk Hanna, Zuazua Rita
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On the Total Set Chromatic Number of Graphs
Theory and Applications of Graphs, 2022 Given a vertex coloring c of a graph, the neighborhood color set of a vertex is defined to be the set of all of its neighbors’ colors. The coloring c is called a set coloring if any two adjacent vertices have different neighborhood color sets.
Mark Anthony C. Tolentino +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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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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Neighbor Distinguishing Colorings of Graphs with the Restriction for Maximum Average Degree
Axioms, 2023 Neighbor distinguishing colorings of graphs represent powerful tools for solving the channel assignment problem in wireless communication networks. They consist of two forms of coloring: neighbor distinguishing edge coloring, and neighbor distinguishing ...
Jingjing Huo +3 more
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