Non-monochromatic Triangles in a 2-Edge-Coloured Graph

Matt DeVos; Jessica McDonald; Amanda Montejano

Non-monochromatic Triangles in a 2-Edge-Coloured Graph

Combinatorics 2018-09-27 v1

Authors: Matt DeVos , Jessica McDonald , Amanda Montejano

Abstract

Let $G = (V,E)$ be a simple graph and let $\{R,B\}$ be a partition of $E$ . We prove that whenever $|E| + \min\{ |R|, |B| \} > { |V| \choose 2 }$ , there exists a subgraph of $G$ isomorphic to $K_3$ which contains edges from both $R$ and $B$ . We conjecture a natural generalization to partitions with more blocks.

Keywords

rainbow coloring bipartite graphs graph coloring

Cite

@article{arxiv.1809.10088,
  title  = {Non-monochromatic Triangles in a 2-Edge-Coloured Graph},
  author = {Matt DeVos and Jessica McDonald and Amanda Montejano},
  journal= {arXiv preprint arXiv:1809.10088},
  year   = {2018}
}

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