# Combinatorics Seminar 2018

Date: Thu, Jan 10, 2019

Time: 10:30 - 11:00

Venue: Xiayuan 211

Title: Homomorphisms of signed subdivisions of $K_4$

Abstract:

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. 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 mapping sparse signed graphs into a given target, 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 graphs to which every signed $K_4$-minor free graph admits a homomorphism.

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