Suppose we have a graph G of the form $G = G1 \cup G2$, and graphs G1 and G2 are defined by $V(G1) = V(G2)$. How can we describe the dynamics of the chromatic number of G in relation to the chromatic numbers of G1 and G2? My prof mentioned in class that it should be the case that $\chi (G) \leq \chi (G1)\times \chi (G2)$ and left it as an exercise to figure out why, but I've been struggling to get to the bottom of it.
2026-03-26 19:20:53.1774552853
Bounds on chromatic number in terms of chromatic numbers of subgraphs.
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