Longest cycles in threshold graphs

AbstractThe length of a longest cycle in a threshold graph is obtained in terms of a largest matching in a specially structured bipartite graph. It can be computed in linear time. As a corollary, Hamiltonian threshold graphs are characterized. This characterization yields Golumbic's characterization and sharpens Minty's characterization. It is also shown that a threshold graph has cycles of length 3, …, l where l is the length of a longest cycle

An extensive English language bibliography on graph theory and its applications

Bibliography on graph theory and its application

Combinatorics

Combinatorics is a fundamental mathematical discipline that focuses on the study of discrete objects and their properties. The present workshop featured research in such diverse areas as Extremal, Probabilistic and Algebraic Combinatorics, Graph Theory, Discrete Geometry, Combinatorial Optimization, Theory of Computation and Statistical Mechanics. It provided current accounts of exciting developments and challenges in these fields and a stimulating venue for a variety of fruitful interactions. This is a report on the meeting, containing extended abstracts of the presentations and a summary of the problem session

Threshold graph limits and random threshold graphs

We study the limit theory of large threshold graphs and apply this to a variety of models for random threshold graphs. The results give a nice set of examples for the emerging theory of graph limits.Comment: 47 pages, 8 figure