34 citations · 188 across the 74 of their papers we have counts for
5 papers · 1 filter
Excluding A Grid Minor In Planar Digraphs
Thor Johnson, Neil Robertson, Paul Seymour +1
In [Directed tree-width, J. Combin. Theory Ser. B 82 (2001), 138-154] we introduced the notion of tree-width of directed graphs and presented a conjecture, formulated during discus…
Induced subgraphs of graphs with large chromatic number. IV. Consecutive holes
Alex Scott, Paul Seymour
A hole in a graph is an induced subgraph which is a cycle of length at least four. We prove that for every positive integer k, every triangle-free graph with sufficiently large chr…
Induced subgraphs of graphs with large chromatic number. III. Long holes
Maria Chudnovsky, Alex Scott, Paul Seymour
We prove a 1985 conjecture of Gyárfás that for all , every graph with sufficiently large chromatic number contains either a complete subgraph with vertices or an induce…
Unavoidable induced subgraphs in large graphs with no homogeneous sets
Maria Chudnovsky, Ringi Kim, Sang-il Oum +1
A homogeneous set of an -vertex graph is a set of vertices () such that every vertex not in is either complete or anticomplete to . A graph is called…
Cyclically five-connected cubic graphs
Neil Robertson, P. D. Seymour, Robin Thomas
A cubic graph is cyclically 5-connected if is simple, 3-connected, has at least 10 vertices and for every set of edges of size at most four, at most one component of $G…