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Potentially K m - G -graphical sequences: A survey

Chunhui LaiLili Hu — 2009

Czechoslovak Mathematical Journal

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...

On potentially K 5 - H -graphic sequences

Lili HuChunhui LaiPing Wang — 2009

Czechoslovak Mathematical Journal

Let K m - H be the graph obtained from K m by removing the edges set E ( H ) of H where H is a subgraph of K m . In this paper, we characterize the potentially K 5 - P 4 and K 5 - Y 4 -graphic sequences where Y 4 is a tree on 5 vertices and 3 leaves.

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