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<p>The dicycle and score (outdegree) structures of tournaments and multipartite tournaments have been studied extensively over past decades. Some classical results include Landau’s [<CitationRef CitationID="CR13">13</CitationRef>], Moon’s [<CitationRef CitationID="CR15">15</CitationRef>] and Bagga and Beineke’s [<CitationRef CitationID="CR2">2</CitationRef>] theorems. In this paper, we extend these results to orientations of a large family of graphs known as the extensions of graphs, which are a natural generalisation of complete multipartite graphs.</p>

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Extensions of Moon’s and Bagga and Beineke’s theorems on dicycle and score (outdegree) structures of tournaments

  • 期刊论文

  • 发表日期：

    2025年12月15日

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  • H. W. Willie Wong,
  • E. G. Tay

摘要

The dicycle and score (outdegree) structures of tournaments and multipartite tournaments have been studied extensively over past decades. Some classical results include Landau’s [13], Moon’s [15] and Bagga and Beineke’s [2] theorems. In this paper, we extend these results to orientations of a large family of graphs known as the extensions of graphs, which are a natural generalisation of complete multipartite graphs.