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arXiv · 2506.22269

Density of Traceable Graphs

Michal Dvořák·Dušan Knop·Michal Opler·Jan Pokorný·Ondřej Suchý·Krisztina Szilágyi
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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.

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Michal Dvořák, Dušan Knop, Michal Opler, Jan Pokorný, Ondřej Suchý, Krisztina Szilágyi. 2025-09-02. Density of Traceable Graphs. https://arxiv.org/abs/2506.22269

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