Fractional chromatic numbers of tensor products of three graphs

Jimeng Xiao; Huajun Zhang; Shenggui Zhang

doi:10.1016/j.disc.2019.01.017

Fractional chromatic numbers of tensor products of three graphs

Jimeng Xiao, Huajun Zhang, Shenggui Zhang

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

The tensor product (G₁,G₂,G₃) of graphs G₁, G₂ and G₃ is defined by V(G₁,G₂,G₃)=V(G₁)×V(G₂)×V(G₃)and E(G₁,G₂,G₃)=((u₁,u₂,u₃),(v₁,v₂,v₃)):|{i:(u_i,v_i)∈E(G_i)}|≥2.Let χ_f(G) be the fractional chromatic number of a graph G. In this paper, we prove that if one of the three graphs G₁, G₂ and G₃ is a circular clique, χ_f(G₁,G₂,G₃)=min{χ_f(G₁)χ_f(G₂),χ_f(G₁)χ_f(G₃),χ_f(G₂)χ_f(G₃)}.

Original language	English
Pages (from-to)	1310-1317
Number of pages	8
Journal	Discrete Mathematics
Volume	342
Issue number	5
DOIs	https://doi.org/10.1016/j.disc.2019.01.017
State	Published - May 2019

Keywords

Circular clique
Direct product
Fractional chromatic number
Fractional clique number
Tensor product

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10.1016/j.disc.2019.01.017

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@article{95fe149225b8430a8f9c9a77c055e5eb,

title = "Fractional chromatic numbers of tensor products of three graphs",

abstract = "The tensor product (G1,G2,G3) of graphs G1, G2 and G3 is defined by V(G1,G2,G3)=V(G1)×V(G2)×V(G3)and E(G1,G2,G3)=((u1,u2,u3),(v1,v2,v3)):|{i:(ui,vi)∈E(Gi)}|≥2.Let χf(G) be the fractional chromatic number of a graph G. In this paper, we prove that if one of the three graphs G1, G2 and G3 is a circular clique, χf(G1,G2,G3)=min{χf(G1)χf(G2),χf(G1)χf(G3),χf(G2)χf(G3)}.",

keywords = "Circular clique, Direct product, Fractional chromatic number, Fractional clique number, Tensor product",

author = "Jimeng Xiao and Huajun Zhang and Shenggui Zhang",

note = "Publisher Copyright: {\textcopyright} 2019 Elsevier B.V.",

year = "2019",

month = may,

doi = "10.1016/j.disc.2019.01.017",

language = "英语",

volume = "342",

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journal = "Discrete Mathematics",

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publisher = "Elsevier B.V.",

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}

TY - JOUR

T1 - Fractional chromatic numbers of tensor products of three graphs

AU - Xiao, Jimeng

AU - Zhang, Huajun

AU - Zhang, Shenggui

PY - 2019/5

Y1 - 2019/5

N2 - The tensor product (G1,G2,G3) of graphs G1, G2 and G3 is defined by V(G1,G2,G3)=V(G1)×V(G2)×V(G3)and E(G1,G2,G3)=((u1,u2,u3),(v1,v2,v3)):|{i:(ui,vi)∈E(Gi)}|≥2.Let χf(G) be the fractional chromatic number of a graph G. In this paper, we prove that if one of the three graphs G1, G2 and G3 is a circular clique, χf(G1,G2,G3)=min{χf(G1)χf(G2),χf(G1)χf(G3),χf(G2)χf(G3)}.

AB - The tensor product (G1,G2,G3) of graphs G1, G2 and G3 is defined by V(G1,G2,G3)=V(G1)×V(G2)×V(G3)and E(G1,G2,G3)=((u1,u2,u3),(v1,v2,v3)):|{i:(ui,vi)∈E(Gi)}|≥2.Let χf(G) be the fractional chromatic number of a graph G. In this paper, we prove that if one of the three graphs G1, G2 and G3 is a circular clique, χf(G1,G2,G3)=min{χf(G1)χf(G2),χf(G1)χf(G3),χf(G2)χf(G3)}.

KW - Circular clique

KW - Direct product

KW - Fractional chromatic number

KW - Fractional clique number

KW - Tensor product

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U2 - 10.1016/j.disc.2019.01.017

DO - 10.1016/j.disc.2019.01.017

M3 - 文章

AN - SCOPUS:85060924749

SN - 0012-365X

VL - 342

SP - 1310

EP - 1317

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 5

ER -

Fractional chromatic numbers of tensor products of three graphs

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Keywords

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