133 research outputs found
A note on heavy cycles in weighted digraphs
A weighted digraph is a digraph such that every arc is assigned a nonnegative
number, called the weight of the arc. The weighted outdegree of a vertex in
a weighted digraph is the sum of the weights of the arcs with as their
tail, and the weight of a directed cycle in is the sum of the weights
of the arcs of . In this note we prove that if every vertex of a weighted
digraph with order has weighted outdegree at least 1, then there exists
a directed cycle in with weight at least . This proves a
conjecture of Bollob\'{a}s and Scott up to a constant factor
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