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On the query complexity of estimating the distance to hereditary graph properties
Carlos Hoppen, Yoshiharu Kohayakawa, Richard Lang +2
Given a family of graphs , we prove that the normalized edit distance of any given graph to being induced -free is estimable with a query complexity t…
Minimum degree conditions for monochromatic cycle partitioning
Dániel Korándi, Richard Lang, Shoham Letzter +1
A classical result of Erdős, Gyárfás and Pyber states that any -edge-coloured complete graph has a partition into monochromatic cycles. Here we determine the min…
Upper density of monochromatic infinite paths
Jan Corsten, Louis DeBiasio, Ander Lamaison +1
We prove that in every -colouring of the edges of there exists a monochromatic infinite path such that has upper density at least ${(12+\sqrt{8})}/{17}…
Monochromatic cycle partitions in random graphs
Richard Lang, Allan Lo
Erdős, Gyárfás and Pyber showed that every -edge-coloured complete graph can be covered by vertex-disjoint monochromatic cycles (independent of ). Here,…
On the list chromatic index of graphs of tree-width 3 and maximum degree at least 7
Richard Lang
Among other results, it is shown that 3-trees are -edge-choosable and that graphs of tree-width 3 and maximum degree at least 7 are -edge-choosable.