Heavy Subgraphs, Stability and Hamiltonicity

• Autorzy: Binlong Li , Bo Ning
• Języki publikacji: EN

Abstrakty

EN

Let G be a graph. Adopting the terminology of Broersma et al. and Čada, respectively, we say that G is 2-heavy if every induced claw (K1,3) of G contains two end-vertices each one has degree at least |V (G)|/2; and G is o-heavy if every induced claw of G contains two end-vertices with degree sum at least |V (G)| in G. In this paper, we introduce a new concept, and say that G is S-c-heavy if for a given graph S and every induced subgraph G′ of G isomorphic to S and every maximal clique C of G′, every non-trivial component of G′ − C contains a vertex of degree at least |V (G)|/2 in G. Our original motivation is a theorem of Hu from 1999 that can be stated, in terms of this concept, as every 2-connected 2-heavy and N-c-heavy graph is hamiltonian, where N is the graph obtained from a triangle by adding three disjoint pendant edges. In this paper, we will characterize all connected graphs S such that every 2-connected o-heavy and S-c-heavy graph is hamiltonian. Our work results in a different proof of a stronger version of Hu’s theorem. Furthermore, our main result improves or extends several previous results.

Słowa kluczowe

EN

heavy subgraphs; hamiltonian graphs; closure theory

Kategorie tematyczne

• 05C45: Eulerian and Hamiltonian graphs
• 05C38: Paths and cycles

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2017
• Tom: 37
• Numer: 3
• Strony: 691-710

Daty

wydano

2017-08-01

otrzymano

2015-06-22

poprawiono

2016-02-05

zaakceptowano

2016-06-11

online

2017-07-06

Twórcy

autor

Binlong Li

• , , Xi’an, , P.R.
• , Pilsen, Czech Republic

autor

Bo Ning

• , , , P.R.

Identyfikatory

DOI

10.7151/dmgt.1967