Closure, clique covering and degree conditions for Hamilton-connectedness in claw-free graphs

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F12%3A43915021" target="_blank" >RIV/49777513:23520/12:43915021 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.disc.2012.02.027" target="_blank" >http://dx.doi.org/10.1016/j.disc.2012.02.027</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.disc.2012.02.027" target="_blank" >10.1016/j.disc.2012.02.027</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Closure, clique covering and degree conditions for Hamilton-connectedness in claw-free graphs

Popis výsledku v původním jazyce

We strengthen the closure concept for Hamilton-connectedness in claw-free graphs, introduced by the second and fourth authors, such that the strong closure of a claw-free graph is the line graph of a multigraph containing at most two triangles or at mostone double edge. Using the concept of strong closure, we prove that a 3-connected claw-free graph G is Hamilton-connected if G satisfies one of the following: (i) G can be covered by at most 5 cliques, (ii) G has minimum degree at least 4 and can be covered by at most 6 cliques, (iii) G has minimum degree at least 6 and can be covered by at most 7 cliques. Finally, by reconsidering the relation between degree conditions and clique coverings in the case of the strong closure, we prove (as a corollary ofa minimum degree sum result) that every 3-connected claw-free graph G of order at least 142 and minimum degree at least (n+50)/8 ) is Hamilton-connected. We also show that our results are asymptotically sharp.

Název v anglickém jazyce

Closure, clique covering and degree conditions for Hamilton-connectedness in claw-free graphs

Popis výsledku anglicky

We strengthen the closure concept for Hamilton-connectedness in claw-free graphs, introduced by the second and fourth authors, such that the strong closure of a claw-free graph is the line graph of a multigraph containing at most two triangles or at mostone double edge. Using the concept of strong closure, we prove that a 3-connected claw-free graph G is Hamilton-connected if G satisfies one of the following: (i) G can be covered by at most 5 cliques, (ii) G has minimum degree at least 4 and can be covered by at most 6 cliques, (iii) G has minimum degree at least 6 and can be covered by at most 7 cliques. Finally, by reconsidering the relation between degree conditions and clique coverings in the case of the strong closure, we prove (as a corollary ofa minimum degree sum result) that every 3-connected claw-free graph G of order at least 142 and minimum degree at least (n+50)/8 ) is Hamilton-connected. We also show that our results are asymptotically sharp.

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/1M0545" target="_blank" >1M0545: Institut Teoretické Informatiky</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)

Rok uplatnění

2012

Kód důvěrnosti údajů

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

Název periodika

DISCRETE MATHEMATICS

ISSN

0012-365X

e-ISSN

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Svazek periodika

312

Číslo periodika v rámci svazku

14

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

13

Strana od-do

2177-2189

Kód UT WoS článku

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EID výsledku v databázi Scopus

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