Kathryn Fraughnaugh

Path assignment for call routing: an application of tabu search

We describe an implementation of tabu search that solves the path assignment problem, which is the problem of routing video data through an undercapacitated telecommunications network. Two versions of the tabu search were studied. Our results compare very favourably with those from other methods.

The Number of Dependent Arcs in an Acyclic Orientation

LetGbe a graph withnnodes,eedges, chromatic number?, and girthg. In an acyclic orientation ofG, an arc isdependentif its reversal creates a cycle. It is well known that if?

Size in maximal triangle-free graphs and minimal graphs of diameter 2

Abstract A triangle-free graph is maximal if the addition of any edge creates a triangle. For n ⩾ 5, we show there is an n -node m -edge maximal triangle-free graph if and only if it is complete bipartite or 2 n − 5 ⩽ m ⩽⌊( n − 1) 2 /4⌋ + 1. A diameter 2 graph is minimal if the deletion of any edge increases the diameter. We show that a triangle-free graph is maximal if and only if it is minimal of diameter 2. For n > n o where n o is a vastly huge number, Furedi showed that an n -node nonbipartite minimal diameter 2 graph has at most ⌊( n − 1) 2 /4⌋ + 1 edges. We demonstrate that n 0 ⩾ 6 by producing a 6-node nonbipartite minimal diameter 2 graph with 8 edges.

Finding Independent Sets in Triangle-free Graphs

Finding a maximum independent set in a graph is well known to be an

The Domination Number of Cubic Graphs with Girth at least Five

NP

Conditional Chromatic Numbers with Forbidden Cycles

-complete problem. Here an

Heuristics for efficient classification

O(n^2)

Lower bounds on size and independence in K 4 -free graphs

-time algorithm that finds an independent set of order at least

P3-Connected Graphs of Minimum Size.

(6n-m)/13

Domination of Graphs with Maximum Degree Three

in a triangle-free graph with