5 citations · 15 across the 13 of their papers we have counts for
13 papers · 1 filter
A survey of -boundedness
Alex Scott, Paul Seymour
If a graph has bounded clique number, and sufficiently large chromatic number, what can we say about its induced subgraphs? András Gyárfás made a number of challenging conjectures…
Sparse graphs with no polynomial-sized anticomplete pairs
Maria Chudnovsky, Jacob Fox, Alex Scott +2
A graph is "-free" if it has no induced subgraph isomorphic to . A conjecture of Conlon, Fox and Sudakov states that for every graph , there exists such that in ever…
Proof of the Kalai-Meshulam conjecture
Maria Chudnovsky, Alex Scott, Paul Seymour +1
Let be a graph, and let be the sum of , over all stable sets . If is a cycle with length divisible by three, then . Motivated by topologica…
Pure pairs. I. Trees and linear anticomplete pairs
Maria Chudnovsky, Alex Scott, Paul Seymour +1
The Erdos-Hajnal Conjecture asserts that for every graph H there is a constant c > 0 such that every graph G that does not contain H as an induced subgraph has a clique or stable s…
Induced subgraphs of graphs with large chromatic number. XIII. New brooms
Alex Scott, Paul Seymour
Gyárfás and Sumner independently conjectured that for every tree , the class of graphs not containing as an induced subgraph is -bounded, that is, the chromatic numbers o…
Size reconstructibility of graphs
Carla Groenland, Hannah Guggiari, Alex Scott
The deck of a graph is given by the multiset of (unlabelled) subgraphs . The subgraphs are referred to as the cards of . Brown and Fenner recently s…