منابع مشابه
Edge cycle extendable graphs
A graph is edge cycle extendable if every cycle C that is formed from edges and one chord of a larger cycle C is also formed from edges and one chord of a cycle C ′ of length one greater than C with V (C ) ⊆ V (C). Edge cycle extendable graphs are characterized by every block being either chordal (every nontriangular cycle has a chord) or chordless (no nontriangular cycle has a chord); equivale...
متن کاملBipartite matching extendable graphs
Matching extendability is significant in graph theory and its applications. The basic notion in this direction is n-extendability introduced by Plummer in 1980. Motivated by the different natures of bipartite matchings and non-bipartite matchings, this paper investigates bipartite-matching extendable (BM-extendable) graphs. A graph G is said to be BM-extendable if every matching M which is a pe...
متن کاملOn critically k-extendable graphs
Let G be a simple connected graph on 2n vertices with a perfect matching. G is k-extendable if for any set M of k independent edges, there exists a perfect matching in G containing all the edges of M. G is critically k-extendable if G is k-extendable but G + uv is not k-extendable for any non-adjacent pair of vertices u and v of G. The problem that arises is that of characterizing k-extendable ...
متن کاملOn almost 1-extendable graphs
A graph G is 1-extendable or almost 1-extendable if every edge is contained in a perfect or almost perfect matching of G, respectively. Let d ≥ 3 be an integer, and let G be a graph of order n with exactly one odd component such that the degree of each vertex is either d or d + 1. If G is not almost 1-extendable, then we prove that n ≥ 2d + 5. In the special case that d ≥ 4 is even and G is a d...
متن کاملLexicographic Product of Extendable Graphs
Lexicographic product G◦H of two graphs G and H has vertex set V (G)×V (H) and two vertices (u1, v1) and (u2, v2) are adjacent whenever u1u2 ∈ E(G), or u1 = u2 and v1v2 ∈ E(H). If every matching of G of size k can be extended to a perfect matching in G, then G is called k-extendable. In this paper, we study matching extendability in lexicographic product of graphs. The main result is that the l...
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ژورنال
عنوان ژورنال: Discussiones Mathematicae Graph Theory
سال: 2020
ISSN: 1234-3099,2083-5892
DOI: 10.7151/dmgt.2308