# 1月18日 王周宁馨博士学术报告（数学与统计学院）

　　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.

/