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Currently displaying 1 – 2 of 2

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Real-time feedback control of computer network based on predicted state estimation.

Ahmed, N.U.; Song, Hui — 2005

Mathematical Problems in Engineering

On short cycles in triangle-free oriented graphs

Yurong Ji; Shufei Wu; Hui Song — 2018

Czechoslovak Mathematical Journal

An orientation of a simple graph is referred to as an oriented graph. Caccetta and Häggkvist conjectured that any digraph on $n$ vertices with minimum outdegree $d$ contains a directed cycle of length at most $⌈ n / d ⌉$ . In this paper, we consider short cycles in oriented graphs without directed triangles. Suppose that $α_{0}$ is the smallest real such that every $n$ -vertex digraph with minimum outdegree at least $α_{0} n$ contains a directed triangle. Let $ϵ < (3 - 2 α_{0}) / (4 - 2 α_{0})$ be a positive real. We show that if $D$ is an oriented graph without...

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