报告人：侯新民副教授，中国科学技术大学
报告时间： 2017年6月11日9:30
报告地点：数计学院4号楼229室
报告题目：Turan number and decomposition number of intersecting odd cycles
报告摘要：Given a graph $H$, the Turan function $ex(n;H)$ is the maximum number of edges in a graph on $n$ vertices that does not contain $H$ as a subgraph. Let $s, t$ be integers and let $H_{s,t}$ be a graph consisting of $s$ triangles and $t$ cycles of odd lengths at least 5 which intersect in exactly one common vertex. Let $\phi(n, H)$ be the smallest integer such that, for all graphs $G$ on $n$ vertices, the edge set $E(G)$ can be partitioned into at most $\phi(n, H)$ parts, of which every part either is a single edge or forms a graph isomorphic to $H$. Pikhurko and Sousa conjectured that $\phi(n, H) = ex(n;H)$ for all $\chi(G)\ge 3$ and all sufficiently large $n$. In this talk, we will survey the works related to the Turan function and decomposition number of $H_{s,t}$.
(Cowork with QIU Yu and LIU Boyuan)
报告人：颜娟副教授，新疆大学
报告时间： 2017年6月11日10:30
报告地点：数计学院4号楼229室
报告题目：A problem about bisections of graphs
报告摘要：Bollobàs and Scott conjectured that every graph G has a balanced bipartite spanning subgraph H such that for each v∈V(G), dh(v)≧(dG(v)-1)/2,. In this talk, we show that every graphic sequence has a realization for which this Bollobàs-Scott conjecture holds, confirming a conjecture of Hartke and Seacrest. On the other hand, we use an infinite family of graphs to illustrate that [(dG(v)-1)/2] (rather than((dG(v)-1)/2) may have been the intended lower bound by Bollobàs and Scott.
