Abstract
We show that every vertex in an unbreakable graph is in a disc, where a disc is a chordless cycle, or the complement of a chordless cycle, with at least five vertices. A corollary is that every vertex in a minimal imperfect graph is in a disc.
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This research was supported by NSERC Operating Grant OGP-0137764.
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Hayward, R.B. Discs in unbreakable graphs. Graphs and Combinatorics 11, 249–254 (1995). https://doi.org/10.1007/BF01793011
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DOI: https://doi.org/10.1007/BF01793011