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Removable edges in near‐bipartite bricks.
- Source :
-
Journal of Graph Theory . Jan2025, Vol. 108 Issue 1, p113-135. 23p. - Publication Year :
- 2025
-
Abstract
- An edge e of a matching covered graph G is removable if G−e is also matching covered. The notion of removable edge arises in connection with ear decompositions of matching covered graphs introduced by Lovász and Plummer. A nonbipartite matching covered graph G is a brick if it is free of nontrivial tight cuts. Carvalho, Lucchesi and Murty proved that every brick other than K4 and C6¯ has at least Δ−2 removable edges. A brick G is near‐bipartite if it has a pair of edges {e1,e2} such that G−{e1,e2} is a bipartite matching covered graph. In this paper, we show that in a near‐bipartite brick G with at least six vertices, every vertex of G, except at most six vertices of degree three contained in two disjoint triangles, is incident with at most two nonremovable edges; consequently, G has at least |V(G)|−62 removable edges. Moreover, all graphs attaining this lower bound are characterized. [ABSTRACT FROM AUTHOR]
- Subjects :
- *BRICKS
*TRIANGLES
*EAR
*BIPARTITE graphs
Subjects
Details
- Language :
- English
- ISSN :
- 03649024
- Volume :
- 108
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Journal of Graph Theory
- Publication Type :
- Academic Journal
- Accession number :
- 180925400
- Full Text :
- https://doi.org/10.1002/jgt.23173