Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
157 tokens/sec
GPT-4o
8 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

On pre-Hamiltonian Cycles in Hamiltonian Digraphs (1404.7620v1)

Published 30 Apr 2014 in math.CO

Abstract: Let $D$ be a strongly connected directed graph of order $n\geq 4$. In \cite{[14]} (J. of Graph Theory, Vol.16, No. 5, 51-59, 1992) Y. Manoussakis proved the following theorem: Suppose that $D$ satisfies the following condition for every triple $x,y,z$ of vertices such that $x$ and $y$ are non-adjacent: If there is no arc from $x$ to $z$, then $d(x)+d(y)+d+(x)+d-(z)\geq 3n-2$. If there is no arc from $z$ to $x$, then $d(x)+d(y)+d-(x)+d+(z)\geq 3n-2$. Then $D$ is Hamiltonian. In this paper we show that: If $D$ satisfies the condition of Manoussakis' theorem, then $D$ contains a pre-Hamiltonian cycle (i.e., a cycle of length $n-1$) or $n$ is even and $D$ is isomorphic to the complete bipartite digraph with partite sets of cardinalities $n/2$ and $n/2$.

Summary

We haven't generated a summary for this paper yet.