Let G be a graph with a perfect matching and let n be an integer, 1⩽n<|V(G)|⧸2. Graph G is n-extendable if every matching of size n in G is a subset of a ...
A graph G is said to be claw-free if it contains no induced subgraph isomorphic to the complete bipartite graph K 1, 3 - the so-called 'claw'. Perhaps, the ...
ABSTRACT. A graph G is 2-extendable if it has at least six vertices and every pair of independent edges extends to (i.e., is a subset of) a perfect matching ...
In this paper, we survey a variety of results obtained over the past few years concerning n-extendable graphs.
... graph has a k-factor; and, if a claw-free graph is (2k + 1)-connected, then any k-edge matching can be extended to a perfect matching. Independent sets. edit.
For proofs, constructions and further discussion about extending matchings in claw- ... , Matching extension in claw-free graphs, 1989, (submitted). [39]. , ...
Both theorems imply that every claw-free cubic graph with no cutedge has at least one perfect matching. In 1970s, Lovász and Plummer conjectured that every ...
Let G be a graph with a perfect matching and let n be an integer, 1⩽ n <| V ( G )|⧸2. Graph G is n - extendable if every matching of size n in G is a ...
Since. Edmonds' matching algorithm generalizes to claw-free graphs, one might hope that also Edmonds' matching polytope theorem [9] extends to claw-free graphs, ...
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May 24, 2024 · In this paper, we establish a characterization of all planar cycle-extendable graphs -- in terms of K_2 and four infinite families.