Recognition of chordal graphs and cographs which are Cover-Incomparability graphs
Abstract
Cover-Incomparability graphs (C-I graphs) are an interesting class of graphs from posets. A C-I graph is a graph from a poset $P=(V,\le)$ with vertex set $V$, and the edge-set is the union of edge sets of the cover graph and the incomparability graph of the poset. The recognition of the C-I graphs is known to be NP-complete (Maxová et al., Order 26(3), 229--236(2009)). In this paper, we prove that chordal graphs having at most two independent simplicial vertices are exactly the chordal graphs which are also C-I graphs. A similar result is obtained for cographs as well. Using the structural results of these graphs, we derive linear time recognition algorithms for chordal graphs and cographs which are C-I graphs.
- Publication:
-
arXiv e-prints
- Pub Date:
- July 2023
- DOI:
- 10.48550/arXiv.2307.13964
- arXiv:
- arXiv:2307.13964
- Bibcode:
- 2023arXiv230713964A
- Keywords:
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- Mathematics - Combinatorics;
- Computer Science - Discrete Mathematics;
- 05C75;
- 05C85
- E-Print:
- 17 pages, 7 figures