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Abstract <p> In an undirected graph, a 3-vertex induced subgraph having exactly 2 edges is calledan open triangle (OT). We consider the class of graphs where the difference between the numbersof edges and vertices is a fixed constant<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(c\)</EquationSource> </InlineEquation>. The complete characterization of graphs on at least<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(c+7\)</EquationSource> </InlineEquation> vertices with the maximum number of OTs is obtained for this class.</p>

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On Graphs with Small Number of Edges Having Extremal Number of Open Triangles

  • 期刊论文

  • 发表日期：

    2025年6月1日

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  • A. V. Pyatkin

摘要

Abstract

In an undirected graph, a 3-vertex induced subgraph having exactly 2 edges is calledan open triangle (OT). We consider the class of graphs where the difference between the numbersof edges and vertices is a fixed constant \(c\) . The complete characterization of graphs on at least \(c+7\) vertices with the maximum number of OTs is obtained for this class.