Minimally unbalanced diamond-free graphs and Dyck-paths
Discrete Mathematics
2014-06-27 v2 Combinatorics
Abstract
A -matrix is balanced if it does not contain a submatrix of odd order having exactly two 1's per row and per column. A graph is balanced if its clique-matrix is balanced. No characterization of minimally unbalanced graphs is known, and even no conjecture on the structure of such graphs has been posed, contrarily to what happened for perfect graphs. In this paper, we provide such a characterization for the class of diamond-free graphs and establish a connection between minimally unbalanced diamond-free graphs and Dyck-paths.
Keywords
Cite
@article{arxiv.1406.6494,
title = {Minimally unbalanced diamond-free graphs and Dyck-paths},
author = {N. Apollonio and A. Galluccio},
journal= {arXiv preprint arXiv:1406.6494},
year = {2014}
}