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.
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。