Elsevier

Discrete Mathematics

Volume 342, Issue 5, May 2019, Pages 1310-1317
Discrete Mathematics

Fractional chromatic numbers of tensor products of three graphs

https://doi.org/10.1016/j.disc.2019.01.017Get rights and content
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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

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

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