4 papers · 1 filter
Forbidden induced pairs for perfectness and -colourability of graphs
Maria Chudnovsky, Adam Kabela, Binlong Li +1
We characterise the pairs of graphs such that all -free graphs (distinct from ) are perfect. Similarly, we characterise pairs such that a…
Quasigraphs and skeletal partitions
Tomáš Kaiser, Petr Vrána
We give a new proof of the Skeletal Lemma, which is the main technical tool in our paper on Hamilton cycles in line graphs [T. Kaiser and P. Vrána, Hamilton cycles in 5-connected l…
The hamiltonicity of essentially 9-connected line graphs
Tomáš Kaiser, Petr Vrána
Yang et al. proved that every 3-connected, essentially 11-connected line graph is Hamilton-connected. This was extended by Li and Yang to 3-connected, essentially 10-connected grap…
Equivalent formulation of Thomassen's conjecture using Tutte paths in claw-free graphs
Adam Kabela, Zdeněk Ryjáček, Petr Vrána
We continue studying Thomassen's conjecture (every 4-connected line graph has a Hamilton cycle) in the direction of a recently shown equivalence with Jackson's conjecture (every 2-…