Browsing Combinatorics and Optimization by Subject "pure pairs"
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Pure Pairs VI. Excluding an Ordered Tree.
(Society for Industrial and Applied Mathematics Journal on Discrete Mathematics, 2022-01)A pure pair in a graph G is a pair (Z1,Z2) of disjoint sets of vertices such that either every vertex in Z1 is adjacent to every vertex in Z2, or there are no edges between Z1 and Z2. With Maria Chudnovsky, we recently ... -
Pure pairs. II. Excluding all subdivisions of a graph
(Springer Nature, 2021-06-01)We prove for every graph H there exists ɛ > 0 such that, for every graph G with |G|≥2, if no induced subgraph of G is a subdivision of H, then either some vertex of G has at least ɛ|G| neighbours, or there are two disjoint ... -
Pure pairs. III. Sparse graphs with no polynomial-sized anticomplete pairs
(Wiley, 2020-11)A graph is H-free if it has no induced subgraph isomorphic to H, and |G| denotes the number of vertices of G. A conjecture of Conlon, Sudakov and the second author asserts that: - For every graph H, there exists ∈ > 0 ...