Solution to a problem on hamiltonicity of graphs under Ore- and Fan-type heavy subgraph conditions

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F16%3A43928674" target="_blank" >RIV/49777513:23520/16:43928674 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1007/s00373-015-1619-1" target="_blank" >http://dx.doi.org/10.1007/s00373-015-1619-1</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00373-015-1619-1" target="_blank" >10.1007/s00373-015-1619-1</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Solution to a problem on hamiltonicity of graphs under Ore- and Fan-type heavy subgraph conditions

Popis výsledku v původním jazyce

A graph G is called claw-o-heavy if every induced claw K(1,3) of G has two end-vertices with degree sum at least |V(G)|. For a given graph S, G is called S-f-heavy if for every induced subgraph H of G isomorphic to S and every pair of vertices u, v ELEMENT OF V(H) with d_H(u, v) = 2, max{d(u), d(v)} is greater or equal |V(G)|/2. In this paper, we prove that every 2-connected claw-o-heavy and Z(3)-f -heavy graph is hamiltonian (with two exceptional graphs), where Z(3) is the graph obtained by identifying one end-vertex of a path with 4 vertices with one vertex of a triangle. This result gives a positive answer to a problem proposed Ning and Zhang (Discrete Math 313:1715-1725, 2013), and also implies two previous theorems of Faudree et al. and Chen et al., respectively.

Název v anglickém jazyce

Solution to a problem on hamiltonicity of graphs under Ore- and Fan-type heavy subgraph conditions

Popis výsledku anglicky

A graph G is called claw-o-heavy if every induced claw K(1,3) of G has two end-vertices with degree sum at least |V(G)|. For a given graph S, G is called S-f-heavy if for every induced subgraph H of G isomorphic to S and every pair of vertices u, v ELEMENT OF V(H) with d_H(u, v) = 2, max{d(u), d(v)} is greater or equal |V(G)|/2. In this paper, we prove that every 2-connected claw-o-heavy and Z(3)-f -heavy graph is hamiltonian (with two exceptional graphs), where Z(3) is the graph obtained by identifying one end-vertex of a path with 4 vertices with one vertex of a triangle. This result gives a positive answer to a problem proposed Ning and Zhang (Discrete Math 313:1715-1725, 2013), and also implies two previous theorems of Faudree et al. and Chen et al., respectively.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/EE2.3.30.0038" target="_blank" >EE2.3.30.0038: Nová excelence lidských zdrojů</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2016

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

GRAPHS AND COMBINATORICS

ISSN

0911-0119

e-ISSN

—

Svazek periodika

32

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

JP - Japonsko

Počet stran výsledku

11

Strana od-do

1125-1135

Kód UT WoS článku

000374837800020

EID výsledku v databázi Scopus

2-s2.0-84940544745