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1. It means that you should take each vertex and look at the subgraph consisting of all neighbors of that vertex. Then look at its complement graph, which you get bh erasing all current edges between vertices and adding ijn all missing edges. Look for triangles here, then do this for all other vertices. Share.
10 de abr. de 2018 · A claw is the graph isomorphic to K1,3 K 1, 3, that is, a star graph with three edges, three leaves, and one central vertex. (see below) A graph is claw-free if it does not contain a claw as an induced subgraph. The line graph of G is the intersection graph of the edges of G, that represents the adjacencies between edges of G.
We say G is claw-free if no X ⊆ V(G) is a claw in G. Our objective in this series of papers is to show that every claw-free graph can be built starting from some basic classes by means of some simple constructions. One important subclass of claw-free graphs are the “long circular interval graphs”, the main topic of this paper.
4 de ago. de 2010 · Line graphs are claw-free, and it has long been recognized that claw-free graphs are an interesting generalization of line graphs, sharing some of the same properties. For instance, Minty [16] showed in 1980 that there is a polynomial-time algorithm to find a stable set of maximum weight in a claw-free graph, generalizing the algorithm of Edmonds [9, 10] to find a maximum weight matching in a ...
1 de abr. de 2019 · For a claw-free graph H with c l ( H) = L ( G), we call G the preimage of H. A connected graph Φ is a closed trail if the degree of each vertex in Φ is even. A closed trail Φ in a graph G is called a spanning closed trail (SCT) if V ( G) = V ( Φ), and is called a dominating closed trail (DCT) if E ( G − V ( Φ)) = 0̸.
1 de ene. de 1998 · 70. Lemma 2.3.LetD be a minimal connected dominating set of a claw-free graph. G, and let X be the vertices of D in two or more cliques of the subgraph induced. by D. Then, for any x e X, D- {x ...
1 de nov. de 1991 · A graph is claw-free if it contains no induced subgraph isomorphic to a K 1,3.This paper studies hamiltonicity in two subclasses of claw-free graphs. A claw-free graph is CN-free (claw-free, net-free) if it does not contain an induced subgraph isomorphic to a net (a triangle with a pendant leaf dangling from each vertex).
