Odd Covers of Graphs
Abstract
Graphs are abstractions of many networks around us: social networks or the World Wide Web, to name just a couple. For various applications, there is interest in efficiently encoding a graph for a computer. We address a problem which relates to finding a “smallest” matrix with which to encode a graph. The problem, phrased in terms of a social network, is to find the minimum number of clubs that a given group of people can form under the condition that, if two people are friends, they are in an odd number of clubs together, and otherwise in an even number.
Odd Covers of Graphs
Graphs are abstractions of many networks around us: social networks or the World Wide Web, to name just a couple. For various applications, there is interest in efficiently encoding a graph for a computer. We address a problem which relates to finding a “smallest” matrix with which to encode a graph. The problem, phrased in terms of a social network, is to find the minimum number of clubs that a given group of people can form under the condition that, if two people are friends, they are in an odd number of clubs together, and otherwise in an even number.