Packing $T$-connectors in graphs needs more connectivity

Roman Čada; Adam Kabela; Tomáš Kaiser; Petr Vrána

Packing $T$-connectors in graphs needs more connectivity

Combinatorics 2023-08-16 v2

Authors: Roman Čada , Adam Kabela , Tomáš Kaiser , Petr Vrána

Abstract

Strengthening the classical concept of Steiner trees, West and Wu [J. Combin. Theory Ser. B 102 (2012), 186--205] introduced the notion of a $T$ -connector in a graph $G$ with a set $T$ of terminals. They conjectured that if the set $T$ is $3k$ -edge-connected in $G$ , then $G$ contains $k$ edge-disjoint $T$ -connectors. We disprove this conjecture by constructing infinitely many counterexamples for $k=1$ and for each even $k$ .

Keywords

graph connectivity graph theory spanning trees

Cite

@article{arxiv.2308.07218,
  title  = {Packing $T$-connectors in graphs needs more connectivity},
  author = {Roman Čada and Adam Kabela and Tomáš Kaiser and Petr Vrána},
  journal= {arXiv preprint arXiv:2308.07218},
  year   = {2023}
}

Packing $T$-connectors in graphs needs more connectivity

Abstract

Keywords

Cite

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