Hamilton‐connected {claw, net}‐free graphs, II

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F23%3A43968316" target="_blank" >RIV/49777513:23520/23:43968316 - isvavai.cz</a>
Result on the web
<a href="https://onlinelibrary.wiley.com/doi/10.1002/jgt.22907" target="_blank" >https://onlinelibrary.wiley.com/doi/10.1002/jgt.22907</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1002/jgt.22907" target="_blank" >10.1002/jgt.22907</a>

Result language
angličtina
Original language name
Hamilton‐connected {claw, net}‐free graphs, II
Original language description
In the first one in this series of two papers, we have proved that every 3‐connected {K(1,3), N(1,3,3)}‐free graph is Hamilton‐connected. In this paper, we continue in this direction by proving that every 3‐connected {K(1,3), X}‐free graph, where X ∈ {N(1,1,5), N(2,2,3)}, is Hamilton‐connected (where N(i,j,k) is the graph obtained by attaching endvertices of three paths of lengths i, j, k to a triangle). This together with a previous result of other authors completes the characterization of forbidden induced generalized nets implying Hamilton-connectedness of a 3‐connected claw‐free graph. We also discuss remaining open cases in a full characterization of connected graphs X such that every 3‐connected {K(1,3), X}‐free graph is Hamilton‐connected.
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
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA20-09525S" target="_blank" >GA20-09525S: Structural properties of graph classes characterized by forbidden subgraphs</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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