Common domination perfect graphs
Magda Dettlaff, Michael A. Henning, Jerzy Topp

TL;DR
This paper characterizes common domination perfect graphs by identifying ten forbidden induced subgraphs, expanding the understanding of domination and independence properties in graph theory.
Contribution
It introduces the concept of common domination perfect graphs and provides a forbidden subgraph characterization for this class.
Findings
Characterization of common domination perfect graphs
Identification of ten forbidden induced subgraphs
Extension of domination and independence concepts
Abstract
A dominating set in a graph is a set of vertices such that every vertex that does not belong to is adjacent to a vertex in . The domination number of is the minimum cardinality of a dominating set of . The common independence number of is the greatest integer such that every vertex of belongs to some independent set of cardinality at least~. The common independence number is squeezed between the independent domination number and the independence number of , that is, . A graph is domination perfect if for every induced subgraph of . We define a graph as common domination perfect if for every induced subgraph of . We provide a characterization of common domination perfect graphs in terms of…
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Taxonomy
TopicsAdvanced Graph Theory Research
