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math.CO2017★ 47 cited
Improper Colourings inspired by Hadwiger's Conjecture
Jan van den Heuvel, David R. Wood
Hadwiger's Conjecture asserts that every -minor-free graph has a proper -colouring. We relax the conclusion in Hadwiger's Conjecture via improper colourings. We prove t…
cs.LO2017★ 5 cited
Model-Checking for Successor-Invariant First-Order Formulas on Graph Classes of Bounded Expansion
Jan van den Heuvel, Stephan Kreutzer, Michał Pilipczuk +3
A successor-invariant first-order formula is a formula that has access to an auxiliary successor relation on a structure's universe, but the model relation is independent of the pa…