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Paths in interval graphs and circular arc graphs. (English) Zbl 0777.05081
Interval graphs and circular arc graphs are intersection graphs of intervals on a line resp. of arcs on a circle. We give polynomial-time algorithms for several path cover problems in such graphs, e.g. for finding a Hamiltonian path in a circular arc graph. Some seemingly similar problems remain open here: Can one find in polynomial time (1) a Hamiltonian cycle in a circular arc graph, (2) a Hamiltonian path with prescribed start vertex in an interval graph?

MSC:
05C45 Eulerian and Hamiltonian graphs
05C85 Graph algorithms (graph-theoretic aspects)
05C38 Paths and cycles
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