Bounding signed series-parallel graphs and cores of signed K 4 -subdivisions

Reza Naserasr (1) , Zhouningxin Wang (1)

1 IRIF (UMR_8243) - Institut de Recherche en Informatique Fondamentale

We study homomorphism properties of signed K4-minor-free graphs. On the one hand we give a necessary and sufficient condition for a signed graph B to admit a homomorphism from any signed K4-minor-free graph and we determine the smallest of all such signed graphs. On the other hand, we characterize the minimal cores that do not belong to the class of signed K4-minor-free graphs. This, in particular, gives a classification of odd-K4's that are cores. Furthermore, we show some applications of our work.

Keywords: graph homomorphisms; signed graphs; minor of graphs; series- parallel graphs

Domains: Computer Science [cs]; Mathematics [math]

Reza Naserasr, Zhouningxin Wang. Bounding signed series-parallel graphs and cores of signed K 4 -subdivisions. Journal of Combinatorial Mathematics and Combinatorial Computing, In press. ⟨hal-02969873⟩