We extend the notion of a potentially H-graphic sequence as follows. Let A and B be nonnegative integer sequences. The sequence pair S = (A,B) is said to be bigraphic if there is some bipartite graph G = (X ∪ Y, E) such that A and B are the degrees of the vertices in X and Y , respectively. If S is a bigraphic pair, let σ(S) denote the sum of the terms in A. Given a bigraphic pair S, and a fixe...

Using degeneration to scrolls, we give an easy proof of non–existence of curves of low genera on general surfaces in P of degree d ≥ 5. We show, along the same lines, boundedness of families of curves of small enough genera on general surfaces in P. We also show that there exist Kobayashi hyperbolic surfaces in P of degree d = 7 (a result so far unknown), and give a new construction of such sur...

A partition of an integer n is graphical if it is the degree sequence of a simple undirected graph It is an open question whether the fraction of partitions of n which are graphical approaches as n approaches in nity A partition is basic if the number of dots in its Ferrers graph is minimum among all partitions with the same rank vector as In this paper we investigate graphical partitions via b...

The following open problem was proposed by Archdeacon: Characterize all graphical sequences π such that some realization of π admits a nowhere-zero 3-flow. This open problem is solved in this paper with the following complete characterization: A graphical sequence π = (d1, d2, . . . , dn) with minimum degree at least two has a realization that admits a nowhere-zero 3-flow if and only if π 6= (3...

We give an upper bound for the largest eigenvalue of a nonregular graph with n vertices and the largest vertex degree ∆.

Let f : X −→ N be an integer function. An f -factor is a spanning subgraph of a graph G = (X,E) whose vertices have degrees defined by f . In this paper, we prove a sufficient condition for the existence of a f -factor which involves the stability number, the minimun degree of G or the connectivity of the graph.

This paper reports the results of a study on the prosodic marking of information status, i.e., whether information is ‘new’ or ‘given’ in the discourse, in Tokyo Japanese noun phrases (NPs). Previous investigations have indicated that such discoursal information is reflected in accent distribution in Dutch NPs, and in degree of accentuation in Italian NPs. An acoustic analysis of Japanese data,...

We propose a new random model of web graphs in which the degree of a vertex depends on its age. We characterize the degree sequence of this model and study its behaviour near the connectivity threshold.

We prove surjectivity of the comparison map from continuous bounded cohomology to continuous cohomology for Hermitian Lie groups with finite center. For general semisimple Lie groups with finite center, the same argument shows that the image of the comparison map contains all the even degree primitive elements. Our proof uses a Hirzebruch type proportionality principle in combination with Gromo...