Primitivity and independent sets in direct products of vertex-transitive graphs

Authors:
Huajun Zhang
Affiliations:
Department of Mathematics Shanghai Normal University Shanghai 200234, People's Republic of China and Department of Mathematics Zhejiang Normal University Jinhua 321004, People's Republic of China
Venue:
Journal of Graph Theory
Year:
2011

Citing 0
Cited 3

Cross-intersecting families and primitivity of symmetric systems

Journal of Combinatorial Theory Series A
The k-independence number of direct products of graphs and Hedetniemi's conjecture

European Journal of Combinatorics
Independent sets in direct products of vertex-transitive graphs

Journal of Combinatorial Theory Series B

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Abstract

We introduce the concept of the primitivity of independent set in vertex-transitive graphs, and investigate the relationship between the primitivity and the structure of maximum independent sets in direct products of vertex-transitive graphs. As a consequence of our main results, we positively solve an open problem related to the structure of independent sets in powers of vertex-transitive graphs. © 2010 Wiley Periodicals, Inc. J Graph Theory 67: 218-225, 2011 © 2011 Wiley Periodicals, Inc.