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Edge coloring signed graphs [PDF]
Discrete Mathematics, 2018 We define a method for edge coloring signed graphs and what it means for such a coloring to be proper. Our method has many desirable properties: it specializes to the usual notion of edge coloring when the signed graph is all-negative, it has a natural ...
Richard Behr
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Maximum Edge-Colorings Of Graphs
Discussiones Mathematicae Graph Theory, 2016 An r-maximum k-edge-coloring of G is a k-edge-coloring of G having a property that for every vertex v of degree dG(v) = d, d ≥ r, the maximum color, that is present at vertex v, occurs at v exactly r times. The r-maximum index χr′(G)$\chi _r^\prime (G)$
Jendrol’ Stanislav +1 more
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Acyclic and star coloring parameters of fractal cubic networks [PDF]
Scientific ReportsInterconnection networks are more vital in telecommunications because of the significant raise in the demand for high-speed networks as a result of the widespread use of computers and the growth of the internet.
C. Renuga +3 more
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Antipodal Edge-Colorings of Hypercubes
Discussiones Mathematicae Graph Theory, 2019 Two vertices of the k-dimensional hypercube Qkare antipodal if they differ in every coordinate. Edges uv and xy are antipodal if u is antipodal to x and v is antipodal to y.
West Douglas B., Wise Jennifer I.
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Strong Edge-Coloring Of Planar Graphs
Discussiones Mathematicae Graph Theory, 2017 A strong edge-coloring of a graph is a proper edge-coloring where each color class induces a matching. We denote by 𝜒's(G) the strong chromatic index of G which is the smallest integer k such that G can be strongly edge-colored with k colors. It is known
Song Wen-Yao, Miao Lian-Ying
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Introduction to dominated edge chromatic number of a graph [PDF]
Opuscula Mathematica, 2021 We introduce and study the dominated edge coloring of a graph. A dominated edge coloring of a graph \(G\), is a proper edge coloring of \(G\) such that each color class is dominated by at least one edge of \(G\).
Mohammad R. Piri, Saeid Alikhani
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Streaming Edge Coloring with Asymptotically Optimal Colors [PDF]
International Colloquium on Automata, Languages and Programming, 2023 Given a graph $G$, an edge-coloring is an assignment of colors to edges of $G$ such that any two edges sharing an endpoint receive different colors. By Vizing's celebrated theorem, any graph of maximum degree $\Delta$ needs at least $\Delta$ and at most $
Soheil Behnezhad, Mohammad Saneian
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Distributed Edge Coloring in Time Polylogarithmic in Δ [PDF]
ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing, 2022 We provide new deterministic algorithms for the edge coloring problem, which is one of the classic and highly studied distributed local symmetry breaking problems. As our main result, we show that a (2Δ - 1)-edge coloring can be computed in time poly log
Alkida Balliu +3 more
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Online edge coloring via tree recurrences and correlation decay [PDF]
Symposium on the Theory of Computing, 2021 We give an online algorithm that with high probability computes a (e/e−1 + o(1))Δ edge coloring on a graph G with maximum degree Δ = ω(logn) under online edge arrivals against oblivious adversaries, making first progress on the conjecture of Bar-Noy ...
Janardhan Kulkarni +4 more
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Locally irregular edge-coloring of subcubic graphs [PDF]
Discrete Applied Mathematics, 2022 A graph is {\em locally irregular} if no two adjacent vertices have the same degree. A {\em locally irregular edge-coloring} of a graph $G$ is such an (improper) edge-coloring that the edges of any fixed color induce a locally irregular graph.
Borut Lužar +5 more
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