Every $3$-connected $\{K_{1,3},\Gamma_3\}$-free graph is Hamilton-connected

Adam Kabela; Zdeněk Ryjáček; Mária Skyvová; Petr Vrána

Every $3$-connected $\{K_{1,3},\Gamma_3\}$-free graph is Hamilton-connected

Combinatorics 2024-11-04 v2

Authors: Adam Kabela , Zdeněk Ryjáček , Mária Skyvová , Petr Vrána

Abstract

We show that every $3$ -connected $\{K_{1,3},\Gamma_3\}$ -free graph is Hamilton-connected, where $\Gamma_3$ 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. Keywords: Hamilton-connected; closure; forbidden subgraph; claw-free; $\Gamma_3$ -free

Keywords

Hamilton-connected closure forbidden subgraph claw-free Γ₃-free

Cite

@article{arxiv.2410.18309,
  title  = {Every $3$-connected $\{K_{1,3},\Gamma_3\}$-free graph is Hamilton-connected},
  author = {Adam Kabela and Zdeněk Ryjáček and Mária Skyvová and Petr Vrána},
  journal= {arXiv preprint arXiv:2410.18309},
  year   = {2024}
}

Comments

arXiv admin note: text overlap with arXiv:2406.03036

Every $3$-connected $\{K_{1,3},\Gamma_3\}$-free graph is Hamilton-connected

Abstract

Keywords

Cite

Comments

Related papers