# 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.

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