On Camby-Plein's Characterization of Domination Perfect Graphs
Vadim Zverovich
TL;DR
This paper critically examines Camby and Plein's 2017 claims on domination perfect graphs, demonstrating that their results are either known, incorrect, or invalid, and provides a correct proof of the 1995 characterization.
Contribution
It clarifies the inaccuracies in Camby and Plein's work and offers a correct proof of the 1995 domination perfect graphs characterization.
Findings
Camby and Plein's results are mostly known or incorrect.
Their proposed counterexamples are invalid.
The paper provides a correct proof of the 1995 characterization.
Abstract
We show that all results stated in [E. Camby, F. Plein, Discrete Appl. Math. 217 (2017) 711-717] are either previously known or incorrect. For example, Camby and Plein claimed to provide counterexamples to the 1995 characterization of domination perfect graphs due to Zverovich and Zverovich; however, these counterexamples are not valid. Moreover, the new characterization of domination perfect graphs proposed in that paper is incorrect. For completeness, we present a relatively brief proof of the 1995 characterization of domination perfect graphs due to Zverovich and Zverovich.
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Taxonomy
TopicsAdvanced Graph Theory Research · Complexity and Algorithms in Graphs · Limits and Structures in Graph Theory