Characterizing minimally n-extendable bipartite graphs
نویسنده
چکیده
In this paper, it is proved that let G be a bipartite graph with bipartition (X, Y ) and with a perfect matching M , let G be an n-extendable graph, then G is minimally n-extendable if and only if, for any two vertices x ∈ X and y ∈ Y such that xy ∈ E(G), there are exactly n internally disjoint (x, y) M-alternating paths P1, P2, . . . , Pn such that Pi (1 i n) starts and ends with edges in E(G)\M . © 2007 Elsevier B.V. All rights reserved.
منابع مشابه
On the structure of minimally n-extendable bipartite graphs
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 structural results on minimally n-extendable bipartite graphs are also given. @ 1999 Elsevier Science ...
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ورودعنوان ژورنال:
- Discrete Mathematics
دوره 308 شماره
صفحات -
تاریخ انتشار 2008