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

Citation

Enright J & Stewart L (2017) Equivalence of the filament and overlap graphs of subtrees of limited trees. Discrete Mathematics and Theoretical Computer Science, 19 (1), Art. No.: 20. https://doi.org/10.23638/DMTCS-19-1-20

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.

Journal
Discrete Mathematics and Theoretical Computer Science: Volume 19, Issue 1