If $X$ is a collection of edges in a graph $G$, let $G/X$ denote the contraction of $X$. Following a question of Oxley and a conjecture of Oporowski, we prove that every projective planar graph $G$ admits an edge partition $\{X,Y\}$ such that $G/X$ and $G/Y$ have tree-width at most three. We prove that every toroidal graph $G$ admits an edge partition $\{X,Y\}$ such that $G/X$ and $G/Y$ have tree-width at most three and four, respectively.
@article{10_37236_2534,
author = {Evan Morgan and Bogdan Oporowski},
title = {Bounding tree-width via contraction on the projective plane and torus},
journal = {The electronic journal of combinatorics},
year = {2015},
volume = {22},
number = {4},
doi = {10.37236/2534},
zbl = {1323.05042},
url = {http://geodesic.mathdoc.fr/articles/10.37236/2534/}
}
TY - JOUR
AU - Evan Morgan
AU - Bogdan Oporowski
TI - Bounding tree-width via contraction on the projective plane and torus
JO - The electronic journal of combinatorics
PY - 2015
VL - 22
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/2534/
DO - 10.37236/2534
ID - 10_37236_2534
ER -
%0 Journal Article
%A Evan Morgan
%A Bogdan Oporowski
%T Bounding tree-width via contraction on the projective plane and torus
%J The electronic journal of combinatorics
%D 2015
%V 22
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/2534/
%R 10.37236/2534
%F 10_37236_2534
Evan Morgan; Bogdan Oporowski. Bounding tree-width via contraction on the projective plane and torus. The electronic journal of combinatorics, Tome 22 (2015) no. 4. doi: 10.37236/2534
