1Department of Mathematics, Simon Fraser University 2Department of Mathematics and Statistics, Auburn University 3UMDI Facultad de Ciencias, Universidad Nacional Autónoma de México
The electronic journal of combinatorics, Tome 26 (2019) no. 3
Let $G = (V,E)$ be a simple graph and let $\{R,B\}$ be a partition of $E$. We prove that whenever $|E| + \mathrm{min}\{ |R|, |B| \} > { |V| \choose 2 }$, there exists a subgraph of $G$ isomorphic to $K_3$ which contains edges from both $R$ and $B$. If instead equality holds, and $G$ has no such subgraph, then we show that $G$ is in one of a few simple classes.
1
Department of Mathematics, Simon Fraser University
2
Department of Mathematics and Statistics, Auburn University
3
UMDI Facultad de Ciencias, Universidad Nacional Autónoma de México
@article{10_37236_8193,
author = {Matt DeVos and Jessica McDonald and Amanda Montejano},
title = {Non-monochromatic triangles in a 2-edge-coloured graph},
journal = {The electronic journal of combinatorics},
year = {2019},
volume = {26},
number = {3},
doi = {10.37236/8193},
zbl = {1416.05103},
url = {http://geodesic.mathdoc.fr/articles/10.37236/8193/}
}
TY - JOUR
AU - Matt DeVos
AU - Jessica McDonald
AU - Amanda Montejano
TI - Non-monochromatic triangles in a 2-edge-coloured graph
JO - The electronic journal of combinatorics
PY - 2019
VL - 26
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/8193/
DO - 10.37236/8193
ID - 10_37236_8193
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%0 Journal Article
%A Matt DeVos
%A Jessica McDonald
%A Amanda Montejano
%T Non-monochromatic triangles in a 2-edge-coloured graph
%J The electronic journal of combinatorics
%D 2019
%V 26
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/8193/
%R 10.37236/8193
%F 10_37236_8193
Matt DeVos; Jessica McDonald; Amanda Montejano. Non-monochromatic triangles in a 2-edge-coloured graph. The electronic journal of combinatorics, Tome 26 (2019) no. 3. doi: 10.37236/8193
