报 告 人：王周宁馨 博士 (巴黎七大)
报告题目：Homomorphisms of signed $K_4$-subdivisions
报告时间：2019年1月18日（周五）上午9:00-10:30
报告地点：静远楼1508报告厅
报告摘要：
A homomorphism of a signed graph $(G, \Sigma)$ to $(H, \Pi)$ is a mapping from the vertices and edges of $G$, respectively, to the vertices and edges of $H$ such that adjacencies, incidences, and signs of closed walks are preserved. Given a class $\mathcal{C}$ of signed graphs, we say signed graph $(H, \Pi)$ homomorphically bounds the class $\mathcal{C}$ if every signed graph in $\mathcal{C}$ admits a homomorphism to $(H, \Pi)$.The core of a signed graph $(G, \Sigma)$ is the minimal subgraph $(G, \Sigma’)$ of this signed graph, such that there exists a homomorphism of $(G, \Sigma)$ to $(G, \Sigma’)$. Motivated by studies on bounds of sparse signed graphs, such as Jaeger-Zhang Conjecture or its bipartite analogue introduced by Charpentier, Naserasr and Sopena, we characterize those signed $K_4$-subdivisions which are cores. We also characterize those signed graphs which would homomorphically bound the class of signed $K_4$-minor free graphs.
This is joint work with Reza Naserasr.