algorithm - Graph labeling in which two cycles share at most one vertex -


good morning. friend gave me interesting graph problem goes below.

given simple graph in 2 cycles share @ 1 vertex, how label edges non negative real number such each vertex, sum of labels of edges incident on not more given constant(lets k) , sum of labels on edges of graph maximum. in advance.

ugh, using sledgehammer kill fly, here goes.

the class of input graphs class of graphs forbid minor:

  *  /|\ * | *  \|/   *

since forbidden minor planar, class has bounded treewidth, , can extract suitable tree decomposition in linear time. general fractional matching polytope half-integral, there exists optimal solution edge labels in {0, 1/2, 1}. can use dynamic programming on tree decomposition find optimal solution in linear time.


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