Some results on fractional edge coloring of graphs

Wang Jihui; Liu Guizhen

Some results on fractional edge coloring of graphs

Wang Jihui^*
, Liu Guizhen

^*此作品的通讯作者

Shandong University
University of Jinan

科研成果: 期刊稿件 › 文章 › 同行评审

1 引用（Scopus）

摘要

A fractional edge coloring of graph G is an assignment of a nonnegative weight ω_M to each matching M of G such that for each edge e we have Σ_M∋eω_M ≥ 1. The fractional edge coloring chromatic number of a graph G, denoted by ξ′_f(G), is the minimum value of Σ_M ω_M(where the minimum is over all fractional edge colorings ω). It is known that for any simple graph G with maximum degree , Δ, Δ ≤ χ′ _f(G) ≤ Δ + 1. And χ′_f/(G) = A + 1 if and only if G is K_2n+1. In this paper, we give some sufficient conditions for a graph G to have χ′_f(G) = Δ. Furthermore we show that the results in this paper is the best possible.

源语言	英语
页（从-至）	249-255
页数	7
期刊	Ars Combinatoria
卷	83
出版状态	已出版 - 4月 2007
已对外发布	是

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N2 - A fractional edge coloring of graph G is an assignment of a nonnegative weight ωM to each matching M of G such that for each edge e we have ΣM∋eωM ≥ 1. The fractional edge coloring chromatic number of a graph G, denoted by ξ′f(G), is the minimum value of ΣM ωM(where the minimum is over all fractional edge colorings ω). It is known that for any simple graph G with maximum degree , Δ, Δ ≤ χ′ f(G) ≤ Δ + 1. And χ′f/(G) = A + 1 if and only if G is K2n+1. In this paper, we give some sufficient conditions for a graph G to have χ′f(G) = Δ. Furthermore we show that the results in this paper is the best possible.

AB - A fractional edge coloring of graph G is an assignment of a nonnegative weight ωM to each matching M of G such that for each edge e we have ΣM∋eωM ≥ 1. The fractional edge coloring chromatic number of a graph G, denoted by ξ′f(G), is the minimum value of ΣM ωM(where the minimum is over all fractional edge colorings ω). It is known that for any simple graph G with maximum degree , Δ, Δ ≤ χ′ f(G) ≤ Δ + 1. And χ′f/(G) = A + 1 if and only if G is K2n+1. In this paper, we give some sufficient conditions for a graph G to have χ′f(G) = Δ. Furthermore we show that the results in this paper is the best possible.

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Some results on fractional edge coloring of graphs

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