Strengthening Rodl's theorem
Abstract
What can be said about the structure of graphs that do not
contain an induced copy of some graph H? Rödl showed in the
1980s that every H-free graph has large parts that are very
sparse or very dense. More precisely, let us say that a graph F
on n vertices is ε-restricted if either F or its complement has
maximum degree at most εn. Rödl proved that for every graph
H, and every ε > 0, every H-free graph G has a linear-sized
set of vertices inducing an ε-restricted graph. We strengthen
Rödl’s result as follows: for every graph H, and all ε > 0,
every H-free graph can be partitioned into a bounded number
of subsets inducing ε-restricted graphs.
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Cite this version of the work
Maria Chudnovsky, Alex Scott, Paul Seymour, Sophie Spirkl
(2023).
Strengthening Rodl's theorem. UWSpace.
http://hdl.handle.net/10012/20111
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