# zbMATH — the first resource for mathematics

A note on degree conditions for traceability in locally claw-free graphs. (English) Zbl 1254.05085
Summary: We say that a set $$S$$ of vertices is traceable in a graph $$G$$ whenever there is a path in $$G$$ containing all vertices of $$S$$. In this paper we study the problem of traceability of a prescribed set of vertices in a locally claw-free graph (i.e. a graph in which some specified vertices are not centers of an induced claw). In particular we give sufficient degree conditions restricted to the given set $$S$$ of vertices for the traceability of $$S$$.

##### MSC:
 05C38 Paths and cycles
##### Keywords:
traceability; degree condition; claw; locally claw-freegraph
Full Text:
##### References:
 [1] Broersma H.J.: Sufficient conditions for hamiltonicity and traceability in K(1,3)-graphs. In: Hamiltonian cycles in graphs and related topics, Ph.D. Thesis, pp. 45–53. University of Twente (1988) [2] Čada R.: The *-closure for graphs and claw-free graphs. Discret. Math. 308(23), 5585–5596 (2008) · Zbl 1186.05076 [3] Čada R., Flandrin E., Li H., Ryjáček Z.: Cycles through given vertices and closures. Discret. Math. 276, 65–80 (2004) · Zbl 1031.05072 [4] Dirac GA.: Some theorems on abstract graphs. Proc. Lond. Math. Soc. 2, 69–81 (1952) · Zbl 0047.17001 [5] Fronček D., Ryjáček Z., Skupień Z.: On traceability and 2-factors in claw-free graphs. Discuss. Math. Graph Theory 24, 55–71 (2004) · Zbl 1055.05094 [6] Frydrych W., Skupień Z.: Non-traceability of large connected claw-free graphs. J. Graph Theory 27(2), 75–86 (1998) · Zbl 0888.05041 [7] Kovářík O., Mulač M., Ryjáček Z.: A note on degree conditions for hamiltonicity in 2-connected claw-free graphs. Discret. Math. 244(1–3), 253–268 (2002) · Zbl 0992.05051 [8] Ryjáček Z.: On a closure concept for claw-free graphs. JCTB 70(2), 217–224 (1997) · Zbl 0872.05032
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.