TY - JOUR
T1 - Fractional chromatic numbers of tensor products of three graphs
AU - Xiao, Jimeng
AU - Zhang, Huajun
AU - Zhang, Shenggui
N1 - Publisher Copyright:
© 2019 Elsevier B.V.
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
UR - http://www.scopus.com/inward/record.url?scp=85060924749&partnerID=8YFLogxK
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 -