Hamiltonian cycles and 2-dominating induced cycles in claw-free graphs

Jinfeng Feng ()

Mathematical Methods of Operations Research, 2009, vol. 69, issue 2, 343-352

Abstract: Let G = (V, E) be a connected graph. For a vertex subset $${S\subseteq V}$$ , G[S] is the subgraph of G induced by S. A cycle C (a path, respectively) is said to be an induced cycle (path, respectively) if G[V(C)] = C (G[V(P)] = P, respectively). The distance between a vertex x and a subgraph H of G is denoted by $${d(x, H)=\min\{d(x,y)\ |\ y\in V(H)\}}$$ , where d(x, y) is the distance between x and y. A subgraph H of G is called 2-dominating if d(x, H) ≤ 2 for all $${x\in V(G)}$$ . An induced path P of G is said to be maximal if there is no induced path P′ satisfying $${V(P)\subset V(P')}$$ and $${V(P')\setminus V(P)\neq \emptyset}$$ . In this paper, we assume that G is a connected claw-free graph satisfying the following condition: for every maximal induced path P of length p ≥ 2 with end vertices u, v it holds: $$ d(u)+d(v)\geq |V(G)|-p+2. $$ Under this assumption, we prove that G has a 2-dominating induced cycle and G is Hamiltonian. Copyright Springer-Verlag 2009

Keywords: Claw; Induced cycle (path); Dominating cycle; Hamiltonian cycle (search for similar items in EconPapers)
Date: 2009
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1007/s00186-008-0263-4 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:mathme:v:69:y:2009:i:2:p:343-352

Ordering information: This journal article can be ordered from
http://www.springer.com/economics/journal/00186

DOI: 10.1007/s00186-008-0263-4

Access Statistics for this article

Mathematical Methods of Operations Research is currently edited by Oliver Stein

More articles in Mathematical Methods of Operations Research from Springer, Gesellschaft für Operations Research (GOR), Nederlands Genootschap voor Besliskunde (NGB)
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().