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A claw-free graph is a graph in which no induced subgraph is a claw; i.e., any subset of four vertices has other than only three edges connecting them in this pattern. Equivalently, a claw-free graph is a graph in which the neighborhood of any vertex is the complement of a triangle-free graph.
16 de may. de 2003 · A graph is claw-free iff it does not contain the complete bipartite graph K_ (1,3) (known as the "claw graph"; illustrated above) as a forbidden induced subgraph. The line graph of any graph is claw-free, as is the complement of any triangle-free graph.
The structure of claw-free graphs Maria Chudnovsky and Paul Seymour Abstract A graph is claw-free if no vertex has three pairwise nonadjacent neighbours. At rst sight, there seem to be a great variety of types of claw-free graphs. For instance, there are line graphs, the graph of the icosahedron, complements of triangle-free graphs, and the Schl a
10 de feb. de 1997 · In this paper we summarize known results on claw-free graphs. The paper is subdivided into the following chapters and sections: 1. Introduction. 2. Paths, cycles, hamiltonicity. 2.1. (a) Preliminaries. 2.2. (b) Degree and neighborhood conditions. 2.3. (c) Local connectivity conditions. 2.4. (d) Further forbidden subgraphs. 2.5. (e) Invariants. 2.6.
- Ralph Faudree, Evelyne Flandrin, Zdeněk Ryjáček
- 1997
1 de sept. de 2008 · A graph is claw-free if no vertex has three pairwise nonadjacent neighbours. In this series of papers we give a structural description of all claw-free graphs. In this paper, we achieve a major part of that goal; we prove that every claw-free graph either belongs to one of a few basic classes, or admits a decomposition in a useful way.
- Maria Chudnovsky, Paul Seymour
- 2008
A claw is a trigraph with four vertices a0,a1,a2,a3, such that {a1,a2,a3} is stable and a0 is complete to {a1,a2,a3}. If X ⊆ V(G) and G|X is a claw, we often loosely say that X is a claw; and if no induced subtrigraph of G is a claw, we say that G is claw-free. It is easy to check that if H is
graph to be Hamiltonian. Similar results for the traceability of connected claw-free graphs are also obtained. Our tools include Ryjaˇcek’s claw-free closure theory and Brousek’s characterization of minimal 2-connected claw-free non-Hamiltonian graphs. Keywords: Hamilton cycles; claw-free graph; clique number; claw-free closure; eigenval-ues
