Graphs satisfying inequality θ(G2)≤θ(G)

Authors:
Ilwon Kang;Suh-Ryung Kim;Yangmi Shin;Yunsun Nam
Affiliations:
Department of Mathematics, Kyung Hee Universtiy, I hoegi-dong, Dongdaemoon-gu, Seoul 130-701, South Korea;Department of Mathematics, Kyung Hee Universtiy, I hoegi-dong, Dongdaemoon-gu, Seoul 130-701, South Korea;Department of Mathematics, Kyung Hee Universtiy, I hoegi-dong, Dongdaemoon-gu, Seoul 130-701, South Korea;Department of Mathematics,Ewha Womans Universtiy, Seoul 120-750, South Korea
Venue:
Discrete Mathematics
Year:
2002

Citing 2
Cited 0

The square of connected S(K1,3)-free graph is vertex pancyclic

Journal of Graph Theory
Dually Chordal Graphs

SIAM Journal on Discrete Mathematics

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Abstract

In this paper, we study the edge clique cover number of squares of graphs. More specifically, we study the inequality θ(G2) ≤ θ(G) where θ(G) is the edge clique cover number of a graph G. We show that any graph G with at most θ(G) vertices satisfies the inequality. Among the graphs with more than θ(G) vertices, we find some graphs violating the inequality and show that dually chordal graphs and power-chordal graphs satisfy the inequality. Especially, we give an exact formula computing θ(T2) for a tree T.