Seminar on Discrete Mathematics: Seymour’s Second Neighborhood Conjecture holds for 7-anti-transitive oriented graphs

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:白延东(西北工业大学)
:2024-01-09 16:30
:海韵园实验楼105报告厅

报告人:白延东(西北工业大学)

 间:20241916:30

 点:海韵园实验楼105报告厅

内容摘要:

An oriented graph is a digraph without 2-cycles. Seymour’s Second Neighborhood Conjecture (SSNC) states that every oriented graph has a vertex satisfying that the cardinality of its second out-neighborhood is not less than that of its first out-neighborhood. A digraph is k-anti-transitive if, for every two vertices u and v, the existence of a directed (u,v)-path of length k implies that u does not dominate v. If SSNC were ture for k-anti-transitive oriented graphs for an arbitrary k, then it would hold for general finite oriented graphs, as every finite oriented graph is k-anti-transitive for k greater than the length of its longest path. So far, SSNC has been verified for k-anti-transitive oriented graphs with k⩽6. We show that SSNC holds for 7-anti-transitive oriented graphs. 

人简介

白延东巴黎第十一大学博士,西北工业大学副教授、硕士生导师。研究方向为图论及其应用,在SIAM J. Discrete Math., European J. Combin., Discrete Math.等期刊发表论文20余篇。获省级教学竞赛一等奖2项、校级教学成果特等奖1项和一等奖2项,2020年获陕西省数学会青年教师优秀论文一等奖,2022年入选西北工业大学“翱翔新星”人才计划,2023年作为主要成员获陕西省高校科学技术研究优秀成果一等奖。

 

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