Coloring graphs with crossings
Bogdan Oporowski, David Zhao
Abstract
We generalize the Five Color Theorem by showing that it extends to graphs with two crossings. Furthermore, we show that if a graph has three crossings, but does not contain K6 as a subgraph, then it is also 5-colorable. We also consider the question of whether the result can be extended to graphs with more crossings.
Create a lesson
Related papers
Combinatorics of hyperplane arrangements and Witten zeta function at the origin
Kam Cheong Au, Kazuhiro Onodera
Proof of the Pach-Tardos conjecture
Lior Gishboliner, Xiangyu Li
Longest cycles intersect linearly in highly connected graphs
Jie Ma, Bo Ning, Ziyuan Zhao
Cutting a convex body into fat parts and approximating Euclidean distance by graph distances
János Pach, Gábor Tardos
A counterexample to the quantum Hedetniemi conjecture
Julius A. Zeiss
Schrijver-Delsarte rigidity in association schemes and undecidability of quantum graph homomorphism
Lorenzo Ciardo, Iris Hebbeker, Gideo Joubert et al.