Every 3-connected {K1,3,Γ3}-free graph is Hamilton-connected

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F25%3A43974829" target="_blank" >RIV/49777513:23520/25:43974829 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.disc.2024.114305" target="_blank" >https://doi.org/10.1016/j.disc.2024.114305</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.disc.2024.114305" target="_blank" >10.1016/j.disc.2024.114305</a>

Result language
angličtina
Original language name
Every 3-connected {K1,3,Γ3}-free graph is Hamilton-connected
Original language description
We show that every 3-connected {K1,3, Γ3}-free graph is Hamilton-connected, where Γ3 is the graph obtained by joining two vertex-disjoint triangles with a path of length 3. This resolves one of the two last open cases in the characterization of pairs of connected forbidden subgraphs implying Hamilton-connectedness. The proof is based on a new closure technique, developed in a previous paper, and on a structural analysis of small subgraphs, cycles and paths in line graphs of multigraphs. The most technical steps of the analysis are computer-assisted.
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
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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