Wang, Xiumei and He, Cheng and Lin, Yixun - Removable edges in near-bricks

dmtcs:600 - Discrete Mathematics & Theoretical Computer Science, July 29, 2013, Vol. 15 no. 2
Removable edges in near-bricks

Authors: Wang, Xiumei and He, Cheng and Lin, Yixun

For a brick apart from a few small graphs, Lovász (1987) proposed a conjecture on the existence of an edge whose deletion results in a graph with only one brick in its tight cut decomposition. Carvalho, Lucchesi, and Murty (2002) confirmed this conjecture by showing the existence of such two edges. This paper generalizes the result obtained by Carvalho et al. to the case of irreducible near-brick, where a graph is irreducible if it contains no induced odd path of length 3 or more. Meanwhile, a lower bound on the number of removable edges of matching-covered bipartite graphs is presented.


Source : oai:HAL:hal-00980764v1
Volume: Vol. 15 no. 2
Section: Graph Theory
Published on: July 29, 2013
Submitted on: October 7, 2011
Keywords: [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]


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