Navigating between packings of graphic sequences

Packing of Graphic Sequences

Let π1 and π2 be graphic n-tuples, with π1 = (d (1) 1 , . . . , d (1) n ) and π2 = (d (2) 1 , . . . , d (2) n ) (they need not be monotone). We say that π1 and π2 pack if there exist edge-disjoint graphs G1 and G2 with vertex set {v1, . . . , vn} such that the degrees of vi in G1 and G2 are d (1) i and d (2) i , respectively. We prove that two graphic n-tuples pack if ∆ ≤ √ 2δn− (δ−1), where ∆ ...

On sequences of lattice packings

Some Problems on Graphic Sequences

A nonnegative integer sequence π is graphic if there is some simple graph G having degree sequence π. In that case, G is said to realize or be a realization of π. A given degree sequence may have many realizations, and it has been of interest to examine the spectrum of properties and parameters that occur across these realizations. In this survey, we present five areas of recent research on gra...

One-Pass Graphic Approximation of Integer Sequences

A variety of network modeling problems begin by generating a degree sequence drawn from a given probability distribution. If the randomly generated sequence is not graphic, we give a new approach for generating a graphic approximation of the sequence. This approximation scheme is fast, requiring only one pass through the sequence, and produces small probability distribution distances for large ...

Contributions to the theory of graphic sequences

Zverovich, I.E. and V.E. Zverovich, Contributions to the theory of graphic sequences, Discrete Mathematics 105 (1992) 293-303. In this article we present a new version of the ErdGs-Gallai theorem concerning graphicness of the degree sequences. The best conditions of all known on the reduction of the number of Erdiis-Gallai inequalities are given. Moreover, we prove a criterion of the bipartite ...