Induced subgraphs of graphs with large chromatic number. VIII. Long odd holes - ScienceDirect
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We devise constant-factor approximation algorithms for finding as many disjoint cycles as
possible from a certain family of cycles in a given planar or bounded-genus graph. Here …

A class of graphs is χ-bounded if there is a function f such that χ (G)≤ f (ω (G)) for every
induced subgraph G of every graph in the class, where χ, ω denote the chromatic number …

We present a new greedy rounding algorithm for the Cycle Packing Problem for uncrossable
cycle families in planar graphs. This improves the best-known upper bound for the integrality …

We prove that for every integer t⩾ 1 there exists a constant ct such that for every K t-minor-
free graph G, and every set S of balls in G, the minimum size of a set of vertices of G …

In this thesis, we derive several results concerning extremal graph theory and probability
theory, focusing particularly on proper colourings of graphs. First, we prove a special case of …