Every 3-connected distance claw-free graph is Hamilton-connected

Authors:
Rao Li;R. H. Schelp
Affiliations:
School of Computer and Information Sciences, Georgia Southwestern State University, Americus, GA;Department of Mathematical Sciences, The University of Memphis, Memphis, TN
Venue:
Discrete Mathematics
Year:
2003

Citing 3
Cited 0

Hamiltonicity in claw-free graphs

Journal of Combinatorial Theory Series A
On a closure concept in claw-free graphs

Journal of Combinatorial Theory Series B
Graph Theory With Applications

Graph Theory With Applications

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Abstract

A graph G is said to be distance claw-free (in DC) if for each vertex v in V(G) the independence number of the subgraph of G induced by the set of vertices at distance i from v is at most 2 for each i ≥ 0. It is shown that every 3-connected graph in DC is hamilton-connected, answering affirmatively a question of Shepherd.