Density of Traceable Graphs
Combinatorics
2025-09-03 v2
Abstract
We establish tight lower and upper bounds on the number of edges in traceable graphs in several classes of dense graphs. A graph is traceable if it has a Hamiltonian path. We show that the bound is: - quadratic for the class of graphs of bounded neighborhood diversity, bounded size of maximum induced matching or bounded cluster vertex deletion number; - n log n for the class of cographs or, more generaly, bounded modular-width, and for the class of bounded distance to cograph; and - sligthly superlinear for the class of bounded shrub-depth.
Keywords
Cite
@article{arxiv.2506.22269,
title = {Density of Traceable Graphs},
author = {Michal Dvořák and Dušan Knop and Michal Opler and Jan Pokorný and Ondřej Suchý and Krisztina Szilágyi},
journal= {arXiv preprint arXiv:2506.22269},
year = {2025}
}