Equivalence of the filament and overlap graphs of subtrees of limited trees

TL;DR

This paper establishes the equivalence of various classes of subtree overlap and filament graphs, generalizing known results and linking them to complements of cochordal-mixed graphs.

Contribution

It extends the known equivalences between subtree overlap and filament graphs to many more classes, unifying them with cochordal-mixed graph complements.

Findings

Many classes of subtree overlap and filament graphs are equivalent.

These classes are characterized as complements of cochordal-mixed graphs.

Results generalize previous specific cases.

Abstract

The overlap graphs of subtrees of a tree are equivalent to subtree filament graphs, the overlap graphs of subtrees of a star are cocomparability graphs, and the overlap graphs of subtrees of a caterpillar are interval filament graphs. In this paper, we show the equivalence of many more classes of subtree overlap and subtree filament graphs, and equate them to classes of complements of cochordal-mixed graphs. Our results generalize the previously known results mentioned above.