Searching expenditure and interval graphs

Authors:
Fedor V. Fomin
Affiliations:
St. Petersburg State University, Mechanical and Mathematical Department, Bibliotechnaya square 2, 198904 St. Petersburg, Russia
Venue:
Discrete Applied Mathematics
Year:
2004

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Abstract

The problem of searching a fugitive in a graph by a team of pursuers is considered. A new criterion of optimal search called the searching expenditure is defined. It is proved that for each graph G, the searching expenditure is equal to the number of edges in the least (with respect to the number of edges) interval graph containing G as a subgraph.