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Every -connected -free graph is Hamilton-connected
Adam Kabela, Zdeněk Ryjáček, Mária Skyvová +1
We show that every -connected -free graph is Hamilton-connected, where is the graph obtained by joining two vertex-disjoint triangles with a path of lengt…
A closure for Hamilton-connectedness in -free graphs
Adam Kabela, Zdeněk Ryjáček, Mária Skyvová +1
We introduce a closure technique for Hamilton-connectedness of -free graphs, where is the graph obtained by joining two vertex-disjoint triangles with a path…
Forbidden induced subgraphs for perfectness of claw-free graphs of independence number at least 4
Christoph Brause, Trung Duy Doan, Přemysl Holub +4
For every graph , we consider the class of all connected -free graphs which are distinct from an odd cycle and have independence number at least , and we show…
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-…
On forbidden induced subgraphs for K_{1,3}-free perfect graphs
Christoph Brause, Přemysl Holub, Adam Kabela +3
Considering connected -free graphs with independence number at least , Chudnovsky and Seymour (2010) showed that every such graph, say , is -colourable where …
The rainbow connection number of 2-connected graphs
Jan Ekstein, Přemysl Holub, Tomáš Kaiser +4
The rainbow connection number of a graph G is the least number of colours in a (not necessarily proper) edge-colouring of G such that every two vertices are joined by a path which…
Pairs of heavy subgraphs for Hamiltonicity of 2-connected graphs
Binlong Li, Zdeněk Ryjáček, Ying Wang +1
Let be a graph on vertices. An induced subgraph of is called heavy if there exist two nonadjacent vertices in with degree sum at least in . We say that $…