Star arboricity relaxed book thickness of $K_n$

Paul C. Kainen

Star arboricity relaxed book thickness of $K_n$

Combinatorics 2024-12-03 v1 Hardware Architecture

Authors: Paul C. Kainen

Abstract

A book embedding of the complete graph $K_n$ needs $\lceil \frac{n}{2} \rceil$ pages and the page-subgraphs can be chosen to be spanning paths (for $n$ even) and one spanning star for $n$ odd. We show that all page-subgraphs can be chosen to be {\rm star forests} by including one extra {\rm cross-cap} page or two new ordinary pages.

Keywords

book embedding complete graph star forest cross-cap page thickness

Cite

@article{arxiv.2412.00971,
  title  = {Star arboricity relaxed book thickness of $K_n$},
  author = {Paul C. Kainen},
  journal= {arXiv preprint arXiv:2412.00971},
  year   = {2024}
}