Results 21 to 30 of about 12,413 (296)
Vertex-Coloring Edge-Weighting of Bipartite Graphs with Two Edge Weights [PDF]
Discrete Mathematics & Theoretical Computer Science, 2016 Let $G$ be a graph and $\mathcal{S}$ be a subset of $Z$. A vertex-coloring $\mathcal{S}$-edge-weighting of $G$ is an assignment of weights by the elements of $\mathcal{S}$ to each edge of $G$ so that adjacent vertices have different sums of incident ...
Hongliang Lu
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Extensions of Vizing fans and Vizing's Theorem in graph edge coloring
, 2022 Graph edge coloring is a well established subject in the field of graph theory. It is one of the basic combinatorial optimization problem: Color the edges of a graph $G$ with as few colors as possible such that each edge receives a color and adjacent ...
Qi, Xuli
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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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Community detection with colored edges [PDF]
2016 IEEE International Symposium on Information Theory (ISIT), 2016 In this paper, we prove a sharp limit on the community detection problem with colored edges. We assume two equal-sized communities and there are $m$ different types of edges. If two vertices are in the same community, the distribution of edges follows $p_i=α_i\log{n}/n$ for $1\leq i \leq m$, otherwise the distribution of edges is $q_i=β_i\log{n}/n$ for
Narae Ryu, Sae-Young Chung
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AVD proper edge-coloring of some families of graphs
International Journal of Mathematics for Industry, 2021 Adjacent vertex-distinguishing proper edge-coloring is the minimum number of colors required for the proper edge-coloring of [Formula: see text] in which no two adjacent vertices are incident to edges colored with the same set of colors.
J. Naveen
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Deterministic distributed edge-coloring with fewer colors [PDF]
Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing, 2018 We present a deterministic distributed algorithm, in the LOCAL model, that computes a $(1+o(1))Δ$-edge-coloring in polylogarithmic-time, so long as the maximum degree $Δ=\tildeΩ(\log n)$. For smaller $Δ$, we give a polylogarithmic-time $3Δ/2$-edge-coloring.
Mohsen Ghaffari 0001 +3 more
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Graphs with coloring redundant edges
Electronic Journal of Graph Theory and Applications, 2016 A graph edge is $d$-coloring redundant if the removal of the edge doesnot change the set of $d$-colorings of the graph. Graphs that are toosparse or too dense do not have coloring redundant edges.
Bart Demoen, Phuong-Lan Nguyen
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Nonrepetitive edge-colorings of trees [PDF]
Discrete Mathematics & Theoretical Computer Science, 2017 A repetition is a sequence of symbols in which the first half is the same as the second half. An edge-coloring of a graph is repetition-free or nonrepetitive if there is no path with a color pattern that is a repetition.
A. Kündgen, T. Talbot
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Discrete Mathematics, 1996 The authors investigate the largest fraction of edges in a 3-regular graph that can be colored in 3 colors. They show that this fraction is always at least 13/15 and sometimes at most 25/27. They investigate the analogous problem for graphs of maximum degree 3 and also for 4-regular graphs with 4 colors instead of 3.
Michael O. Albertson, Ruth Haas
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Properly Edge-colored Theta Graphs in Edge-colored Complete Graphs [PDF]
Graphs and Combinatorics, 2018 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ruonan Li, Hajo Broersma, Shenggui Zhang
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