A note on singular edges and hamiltonicity in claw-free graphs with locally disconnected vertices

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F20%3A43958582" target="_blank" >RIV/49777513:23520/20:43958582 - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/article/10.1007/s00373-020-02144-1" target="_blank" >https://link.springer.com/article/10.1007/s00373-020-02144-1</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00373-020-02144-1" target="_blank" >10.1007/s00373-020-02144-1</a>

Jazyk výsledku

angličtina

Název v původním jazyce

A note on singular edges and hamiltonicity in claw-free graphs with locally disconnected vertices

Popis výsledku v původním jazyce

An edge e of a graph G is called singular if it is not on a triangle and nonsingular otherwise. A vertex is singular if it is adjacent to a singular edge, and nonsingular otherwise. We prove the following. Let G be a connected claw-free graph such that every locally disconnected vertex x of G satisfies the following conditions: (i) if x is nonsingular of degree 4, then x is on an induced cycle of length at least 4 with at most 4 nonsingular edges, (ii) if x is not nonsingular of degree 4, then x is on an induced cycle of length at least 4 with at most 3 nonsingular edges, (iii) if x is of degree 2, then x is singular and x is on an induced cycle C of length at least 4 with at most 2 nonsingular edges such that vertices of degree 2 of C induce in G a path or a cycle. Then G is either hamiltonian, or G belongs to a well-described class of exceptions. Some results on forbidden subgraph conditions for hamiltonicity in 3-connected claw-free graphs are also obtained as immediate corollaries.

Název v anglickém jazyce

A note on singular edges and hamiltonicity in claw-free graphs with locally disconnected vertices

Popis výsledku anglicky

An edge e of a graph G is called singular if it is not on a triangle and nonsingular otherwise. A vertex is singular if it is adjacent to a singular edge, and nonsingular otherwise. We prove the following. Let G be a connected claw-free graph such that every locally disconnected vertex x of G satisfies the following conditions: (i) if x is nonsingular of degree 4, then x is on an induced cycle of length at least 4 with at most 4 nonsingular edges, (ii) if x is not nonsingular of degree 4, then x is on an induced cycle of length at least 4 with at most 3 nonsingular edges, (iii) if x is of degree 2, then x is singular and x is on an induced cycle C of length at least 4 with at most 2 nonsingular edges such that vertices of degree 2 of C induce in G a path or a cycle. Then G is either hamiltonian, or G belongs to a well-described class of exceptions. Some results on forbidden subgraph conditions for hamiltonicity in 3-connected claw-free graphs are also obtained as immediate corollaries.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

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

Rok uplatnění

2020

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

36

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

JP - Japonsko

Počet stran výsledku

13

Strana od-do

665-677

Kód UT WoS článku

000518137000001

EID výsledku v databázi Scopus

2-s2.0-85080069039