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

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
A note on singular edges and hamiltonicity in claw-free graphs with locally disconnected vertices
Original language description
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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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