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Removable ears of 1-extendable graphs

✍ Scribed by Shaohui Zhai; Xiaofeng Guo

Book ID
107347196
Publisher
Academy of Mathematics and Systems Science, Chinese Academy of Sciences
Year
2010
Tongue
English
Weight
200 KB
Volume
23
Category
Article
ISSN
1009-6124

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Let G be a simple connected graph on 2n vertices with perfect matching. For a given positive integer k (0 , then either G is bipartite or the connectivity of G is at least 2k. As a corollary, we show that if G is a maximal k-extendable graph on 2n vertices with n + 2 6 2k + 1, then G is Kn;n if k +

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It is proved that, in a minimal n-extendable bipartite graph, the subgraph induced by the edges both ends of which have degree at least n + 2 is a forest. As a consequence, every minimal n-extendable bipartite graph has at least 2n + 2 vertices of degree n + 1. This result is sharp. Some other struc