A closure for Hamilton-connectedness in {K1,3,Γ3}-free graphs

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F24%3A43972344" target="_blank" >RIV/49777513:23520/24:43972344 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.disc.2024.114154" target="_blank" >https://doi.org/10.1016/j.disc.2024.114154</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.disc.2024.114154" target="_blank" >10.1016/j.disc.2024.114154</a>

Result language
angličtina
Original language name
A closure for Hamilton-connectedness in {K1,3,Γ3}-free graphs
Original language description
We introduce a closure technique for Hamilton-connectedness of {K(1,3),Gamma(3)}-free graphs, where Gamma(3) is the graph obtained by joining two vertex-disjoint triangles with a path of length 3. The closure turns a claw-free graph into a line graph of a multigraph while preserving its (non)-Hamilton-connectedness. The most technical parts of the proof are computer-assisted.The main application of the closure is given in a subsequent paper showing that every 3-connected {K(1,3),Gamma(3)}-free graph is Hamilton-connected, thus resolving one of the two last open cases in the characterization of pairs of connected forbidden subgraphs implying Hamilton-connectedness.
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
<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
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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