?報(bào)告人：蔡建生 教授

報(bào)告題目：Quasi-pancyclicity of regular multipartite tournaments

報(bào)告時(shí)間：2025年10月17日（周五）上午 09：00

報(bào)告地點(diǎn)：云龍校區(qū)6號(hào)樓304會(huì)議室

主辦單位：數(shù)學(xué)與統(tǒng)計(jì)學(xué)院、數(shù)學(xué)研究院、科學(xué)技術(shù)研究院

報(bào)告人簡(jiǎn)介：

蔡建生，濰坊學(xué)院數(shù)學(xué)與統(tǒng)計(jì)學(xué)院教授，中國(guó)工業(yè)與應(yīng)用數(shù)學(xué)學(xué)會(huì)圖論組合及其應(yīng)用專(zhuān)業(yè)委員會(huì)常務(wù)委員、中國(guó)工業(yè)與應(yīng)用數(shù)學(xué)學(xué)會(huì)信息和通訊領(lǐng)域的數(shù)學(xué)專(zhuān)業(yè)委員會(huì)委員、山東省數(shù)學(xué)會(huì)高等數(shù)學(xué)專(zhuān)業(yè)委員會(huì)常務(wù)理事、濰坊市五一勞動(dòng)獎(jiǎng)?wù)芦@得者。長(zhǎng)期從事圖論和組合數(shù)學(xué)的研究，發(fā)表本專(zhuān)業(yè)學(xué)術(shù)論文80余篇，主持和參與國(guó)家自然科學(xué)基金項(xiàng)目多項(xiàng)，主持山東省自然科學(xué)基金項(xiàng)目多項(xiàng)。獲得山東省自然科學(xué)三等獎(jiǎng)一項(xiàng)，獲得山東省高等學(xué)校優(yōu)秀科研成果獎(jiǎng)多項(xiàng)。

報(bào)告摘要：

The study of arc-pancyclicity of tournaments has a long history. Alspach proved that every arc of a regular tournament is in a $k$-cycle for each $k\in \{3,4,\ldots, n \}$.

In this talk, we extend the arc-pancyclicity for regular tournaments to multipartite tournaments. we prove that every arc of a regular $c$-partite tournament $T$ with $c\geq 3$ belongs to $c-2$ cycles of pairwise distinct lengths. Moreover, we also proved that for any two partite sets $V_i,V_j$ of $T$ with $[V_i,V_j]\neq \emptyset$, $1\leq i\neq j\leq c$, there is a $(V_j, V_i)$-path that transverses exactly $k$ partite sets for each $k\in \{4, \ldots , c\}$. These results extend Alspach's theorem from regular tournaments to regular multipartite tournaments.