Path coloring explained
In graph theory, path coloring usually refers to one of two problems:
in graph
, in such a way that any two paths of
which share an edge in
receive different colors. Set
and graph
are provided at input. This formulation is equivalent to
vertex coloring the
conflict graph of set
, i.e. a graph with vertex set
and edges connecting all pairs of paths of
which are not edge-disjoint with respect to
.
of paths in
, such that the set of pairs of end-vertices of paths from
is equal to some set or multiset
, called a
set of requests. Set
and graph
are provided at input. This problem is a special case of a more general class of graph routing problems, known as call scheduling.In both the above problems, the goal is usually to minimise the number of colors used in the coloring. In different variants of path coloring,
may be a simple graph,
digraph or
multigraph.
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