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Interval graphs and searching. (English) Zbl 0566.05056
The interval thickness of a graph G is the minimum clique number of all the interval supergraphs of G. The clique number of a graph is the number of nodes of its biggest complete subgraph. On the other hand, the node- search number is the least number of searchers (pebbles) required to clear the ”contaminated” edges of a graph. A contaminated edge is cleared by concurrently having two searchers on both of its endpoints. The ”contamination” may spread from an uncleared edge to a cleared one through an unguarded path. It is proved that for any graph the node- search number is equal to the interval thickness.

MSC:
05C99 Graph theory
68R10 Graph theory (including graph drawing) in computer science
68Q25 Analysis of algorithms and problem complexity
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