Let G = (V, E) be an undirected graph. Design algorithms for the following (in each
case discuss the complexity of your algorithm):
(a) Assume G contains only one cycle. Direct the edges s.t. for each u, indegree(u) [tex]\leq[/tex] 1.
(b) Determine whether it is possible to direct the edges of G s.t. for each u, indegree(u) [tex]\geq[/tex] 1.
If it is possible, your algorithm should provide a way to do so.
(c) Let S be a subset of edges s.t. every cycle of G has at least one edge in S. Find a
minimum size subset S.

Question

03-01-2021
Computers and Technology

Answered

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Let G = (V, E) be an undirected graph. Design algorithms for the following (in each
case discuss the complexity of your algorithm):
(a) Assume G contains only one cycle. Direct the edges s.t. for each u, indegree(u) [tex]\leq[/tex] 1.
(b) Determine whether it is possible to direct the edges of G s.t. for each u, indegree(u) [tex]\geq[/tex] 1.
If it is possible, your algorithm should provide a way to do so.
(c) Let S be a subset of edges s.t. every cycle of G has at least one edge in S. Find a
minimum size subset S.

Sagot :

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