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 ...

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 ...

In this paper, we proposed a new method for phylogenetic analysis, based on graphic representations of DNA sequences. Utilizing the invariants of graphs, we give the distance measure of DNA sequences and define the distance between species. We have chosen mitochondrial DNA sequences of 30 species and constructed their phylogenies successfully. The method does not require sequence alignment and ...

In this paper, we characterize the potentially (K4 − e)-graphic sequences where K4 − e is the graph obtained from K4 by removing one edge. This characterization implies a theorem due to C. H. Lai (Australas. J. Combin. 24 (2001), 123–127) and a characterization of potentially C4graphic sequences due to R. Luo (Ars Combin. 64 (2002), 301–318).

A sequence 1l = (d 1 ,d 2 , ... ,d n) of positive integers is said to be graphic if there exists a simple graph G such that 1£ is the degree sequence of G. For a specified property P of graphs. a sequence 1l = (d 1 ,d 2 • ... • d n) of positive integers is said to be potentially P-graphic if 1l is graphic and there exists a realization of 1l with the property P. In this paper we characterize po...

A sequence of nonnegative integers π is graphic if it is the degree sequence of some graph G. In this case we say that G is a realization of π, and we write π = π(G). A graphic sequence π is potentially H-graphic if there is a realization of π that contains H as a subgraph. Given nonincreasing graphic sequences π1 = (d1, . . . , dn) and π2 = (s1, . . . , sn), we say that π1 majorizes π2 if di ≥...

For given a graph H , a graphic sequence π = (d1, d2, · · · , dn) is said to be potentially H-graphic if there exists a realization of π containing H as a subgraph. In this paper, we characterize the potentially K6 − C5 -graphic sequences .

For given a graph H , a graphic sequence π = (d1, d2, · · · , dn) is said to be potentially H-graphic if there exists a realization of π containing H as a subgraph. In this paper, we characterize the potentially K6 − C5 -graphic sequences .