منابع مشابه
A note on k-extendable graphs and independence number
An even order graph G with a perfect matching is k-extendable if for every matching M of size k in G, there exists a perfect matching in G containing all the edges of M. In this note, we estabUsh a necessary and sufficient condition for a graph to be k-extendable in terms of its independence number. All graphs considered in this note are finite, connected, loopless and have no multiple edges. F...
متن کاملCounting perfect matchings in n-extendable graphs
The structural theory of matchings is used to establish lower bounds on the number of perfect matchings in n-extendable graphs. It is shown that any such graph on p vertices and q edges contains at least (n + 1)!/4[q − p − (n − 1)(2 − 3) + 4] different perfect matchings, where is the maximum degree of a vertex in G. © 2007 Elsevier B.V. All rights reserved. MSC: 05C70; 05C40; 05C75
متن کاملSome conditions for n-extendable graphs
Abslracl A Tulle slyle necessary and surricienl condilion lor n-ex'lendable graphs is proposed. Lel G be a conn-ecled graph and lel u and v be lwo verlices or G such lhal dGCu,v) == 2. We derine divergenceex*Cu.v) as an independenl sel conlaining u and v in G[{w) U NGCw)]) * aI'ld ex Cu, v) = max { I Cw) w U,v proved lhal ir ror any lwo verlices u and v or G such 1 and ir G has even order, lhen...
متن کاملCharacterizing minimally n-extendable bipartite graphs
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)...
متن کاملCharacterizing 2k-critical graphs and n-extendable graphs
Let G be a graph with even order. Let M be a matching in G and x1, x2, . . . , x2r , be the M-unsaturated vertices in G. Then G has a perfect matching if and only if there are r independentM-augmenting paths joining the 2r vertices in pairs. LetG be a graph with a perfect matchingM . It is proved that G is 2k-critical if and only if for any 2k vertices u1, u2, . . . , u2k in G, there are k inde...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1996
ISSN: 0012-365X
DOI: 10.1016/0012-365x(95)00042-u