5 citations · 15 across the 13 of their papers we have counts for
36 papers · 1 filter
Clique covers of H-free graphs
Tung Nguyen, Alex Scott, Paul Seymour +1
It takes cliques to cover all the edges of a complete bipartite graph , but how many cliques does it take to cover all the edges of a graph if has no $…
Bipartite graphs with no minor
Maria Chudnovsky, Alex Scott, Paul Seymour +1
A theorem of Mader shows that every graph with average degree at least eight has a minor, and this is false if we replace eight by any smaller constant. Replacing average deg…
Polynomial bounds for chromatic number VII. Disjoint holes
Maria Chudnovsky, Alex Scott, Paul Seymour +1
A hole in a graph is an induced cycle of length at least four, and a -multihole in is a set of pairwise disjoint and nonadjacent holes. It is well known that if does…
Polynomial bounds for chromatic number. III. Excluding a double star
Alex Scott, Paul Seymour, Sophie Spirkl
A double star is a tree with two internal vertices. It is known that the Gyárfás-Sumner conjecture holds for double stars, that is, for every double star , there is a function $…
Polynomial bounds for chromatic number. II. Excluding a star-forest
Alex Scott, Paul Seymour, Sophie Spirkl
The Gyarfas-Sumner conjecture says that for every forest , there is a function such that if is -free then (where are the chromatic number and…
Powers of paths and cycles in tournaments
António Girão, Dániel Korándi, Alex Scott
We show that for every positive integer , any tournament can be partitioned into at most -th powers of paths. This result is tight up to the exponential constant. Mo…