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Potentially K m — G-graphical sequences: A survey

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Abstract

The set of all non-increasing nonnegative integer sequences π = (d(v 1), d(v 2), …, d(v n )) is denoted by NS n . A sequence π ∈ NS n is said to be graphic if it is the degree sequence of a simple graph G on n vertices, and such a graph G is called a realization of π. The set of all graphic sequences in NS n is denoted by GS n . A graphical sequence π is potentially H-graphical if there is a realization of π containing H as a subgraph, while π is forcibly H-graphical if every realization of π contains H as a subgraph. Let K k denote a complete graph on k vertices. Let K m −H be the graph obtained from Km by removing the edges set E(H) of the graph H (H is a subgraph of K m ). This paper summarizes briefly some recent results on potentially K m −G-graphic sequences and give a useful classification for determining σ (H, n).

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Authors and Affiliations

  1. Department of Mathematics, Zhangzhou Teachers College, Zhangzhou, Fujian, 363000, P.R.China

    Chunhui Lai & Lili Hu

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  1. Chunhui Lai
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  2. Lili Hu
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Correspondence to Chunhui Lai.

Additional information

Project Supported by NSF of Fujian(2008J0209), Fujian Provincial Training Foundation for “Bai-Quan-Wan Talents Engineering”, Project of Fujian Education Department and Project of Zhangzhou Teachers College (SK07009).

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Lai, C., Hu, L. Potentially K m — G-graphical sequences: A survey. Czech Math J 59, 1059–1075 (2009). https://doi.org/10.1007/s10587-009-0074-7

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