| Saturday 20 April 2024 | |
| Events for day: Wednesday 06 April 2022 |
| 14:00 - 15:00 Combinatorics and Computing Weekly Seminar Graph Coloring and Homomorphisms to Signed Cycles School MATHEMATICS A graph $G$ is $(2k+1)$-colorable if and only if the graph $T_{2k-1}(G)$, obtained from $G$ by replacing each edge with a path of length $2k-1$, admits a homomorphism to $C_{2k+1}$. Until recently this classic observation had no analogue for $2k$-colorability. However, the development of homomorphisms and coloring of signed graphs has provided room for this and many other analogue studies. With a focus on 4-colorability, we consider the following extension of the "proper coloring" to signed graphs: a signed graph $(G, sigma)$ is said to be ${+1,-1,+2,-2}$-colorable if, using this set of colors, one can get a vertex-coloring $c$ satisfy ... |