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

Result code in 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>

Result on the web

<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>

Result language

angličtina

Original language name

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

Original language description

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.

Czech name

—

Czech description

—

Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

—

Project

<a href="/en/project/1M0545" target="_blank" >1M0545: Institute for Theoretical Computer Science</a><br>

Continuities

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

Publication year

2012

Confidentiality

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

Name of the periodical

DISCRETE MATHEMATICS

ISSN

0012-365X

e-ISSN

—

Volume of the periodical

312

Issue of the periodical within the volume

14

Country of publishing house

NL - THE KINGDOM OF THE NETHERLANDS

Number of pages

13

Pages from-to

2177-2189

UT code for WoS article

—

EID of the result in the Scopus database

—