28 research outputs found
Multicolor and directed edit distance
The editing of a combinatorial object is the alteration of some of its
elements such that the resulting object satisfies a certain fixed property. The
edit problem for graphs, when the edges are added or deleted, was first studied
independently by the authors and K\'ezdy [J. Graph Theory (2008), 58(2),
123--138] and by Alon and Stav [Random Structures Algorithms (2008), 33(1),
87--104]. In this paper, a generalization of graph editing is considered for
multicolorings of the complete graph as well as for directed graphs.
Specifically, the number of edge-recolorings sufficient to be performed on any
edge-colored complete graph to satisfy a given hereditary property is
investigated. The theory for computing the edit distance is extended using
random structures and so-called types or colored homomorphisms of graphs.Comment: 25 page
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