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A survey of the theory of potentially P-graphic and forcibly P-graphic degree sequences

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Combinatorics and Graph Theory

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 885))

Abstract

A sequence π=(d1,…,dp) of length p is said to be graphic if there exists a graph G with V(G)={u1,…,up} such that the degree of ui in G is equal to di, for every i, l≤i≤p; and G is referred to as a realization of π. Let P be an invariant graph theoretic property. A sequence π is said to be potentially P-graphic if there exists a realization of π with the property P; π is said to be forcibly P-graphic if π is graphic and every realization of π has been property P. Indicating the different unified approaches in the theory of potentially P-graphic and forcibly P-graphic sequences, we survey the known results on potentially P-graphic and forcibly P-graphic sequences for various properties P. We provide an extensive bibliography on these topics and mention several unsolved problems and conjectures.

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Rao, S.B. (1981). A survey of the theory of potentially P-graphic and forcibly P-graphic degree sequences. In: Rao, S.B. (eds) Combinatorics and Graph Theory. Lecture Notes in Mathematics, vol 885. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0092288

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