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Given a graph with colored edges, a Hamiltonian cycle is
called alternating if its successive edges differ in color. The problem
of finding such a cycle, even for 2-edge-colored graphs, is trivially
NP-complete, while it is known to be polynomial for 2-edge-colored
complete graphs. In this paper we study the parallel complexity of
finding such a cycle, if any, in 2-edge-colored complete graphs. We give
a new characterization for such a graph admitting an alternating
Hamiltonian cycle which allows...
It is known that finding a perfect matching in a general graph
is
-equivalent to finding a perfect matching
in a 3-regular ( cubic) graph.
In this paper we extend this result to both, planar and bipartite cases.
In particular we prove that the construction
problem for perfect matchings in planar graphs
is as difficult as in the case of planar cubic graphs
like it is known to be the case for the famous Map Four-Coloring problem.
Moreover we prove that the existence and construction...
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