Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1710530 | Applied Mathematics Letters | 2007 | 7 Pages |
Abstract
An outerplane graph is a connected plane graph with all vertices lying on the boundary of its outer face. For a catacondensed benzenoid graph GG, i.e. a 2-connected outerplane graph each inner face of which is a regular hexagon, S. Klavžar and P. Žigert [A min–max result on catacondensed benzenoid graphs, Appl. Math. Lett. 15 (2002) 279–283] discovered that the smallest number of elementary cuts that cover GG equals the dimension of a largest induced hypercube of its resonance graph. In this note, we extend the result to any 2-connected outerplane bipartite graph by applying Dilworth’s min–max theorem on partially ordered sets.
Related Topics
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Authors
Heping Zhang, Haiyuan Yao, Dewu Yang,