47 citations · 678 across the 85 of their papers we have counts for
5 papers · 1 filter
Improper coloring of graphs with no odd clique minor
Dong Yeap Kang, Sang-il Oum
As a strengthening of Hadwiger's conjecture, Gerards and Seymour conjectured that every graph with no odd minor is -colorable. We prove two weaker variants of this con…
Defective colouring of graphs excluding a subgraph or minor
Patrice Ossona de Mendez, Sang-il Oum, David R. Wood
Archdeacon (1987) proved that graphs embeddable on a fixed surface can be -coloured so that each colour class induces a subgraph of bounded maximum degree. Edwards, Kang, Kim, O…
Majority Colourings of Digraphs
Stephan Kreutzer, Sang-il Oum, Paul Seymour +2
We prove that every digraph has a vertex 4-colouring such that for each vertex , at most half the out-neighbours of receive the same colour as . We then obtain several re…
Deciding whether there are infinitely many prime graphs with forbidden induced subgraphs
Robert Brignall, Hojin Choi, Jisu Jeong +1
A homogeneous set of a graph is a set of vertices such that and no vertex in has both a neighbor and a non-neighbor in …
Rank-width: Algorithmic and structural results
Sang-il Oum
Rank-width is a width parameter of graphs describing whether it is possible to decompose a graph into a tree-like structure by `simple' cuts. This survey aims to summarize known al…