A Sufficient and Necessary Condition for the Forcing Number of a Bipartite Graph Being Equal to the Minimum Number of Trailing Vertices

Authors:
Hongwei Wang
Affiliations:
Department of Mathematics, Linyi Normal University, Linyi, China 276005
Venue:
COCOA '09 Proceedings of the 3rd International Conference on Combinatorial Optimization and Applications
Year:
2009

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Abstract

Riddle [15] showed that the forcing number of a bipartite graph is bounded blow by the minimum number of trailing vertices of the ordering of a color set. In the present work, we improve the trailing-vertex method by Riddle and obtain a necessary condition for the matching forcing number of a bipartite graph being equal to a given natural number k ; furthermore, we give a sufficient and necessary condition for the minimum forcing number of bipartite graph being equal to the minimum number of trailing vertices of all standard orderings of a color set.