The smallest degree sum that yields graphic sequences with a Z3-connected realization

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Abstract

A non-increasing sequence π=(d1,d2,,dn) of non-negative integers is said to be graphic if it is the degree sequence of a simple graph G on n vertices. Let A be an (additive) Abelian group. An extremal problem for a graphic sequence to have an A-connected realization is considered as follows: determine the smallest even integer σ(A,n) such that each graphic sequence π=(d1,d2,,dn) with dn2 and σ(π)=d1+d2++dnσ(A,n) has an A-connected realization. In this paper, we determine σ(Z3,n) for n5.

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Supported by the National Natural Science Foundation of China (Grant No. 11161016).