Coloring the Cartesian sum of graphs (Q998323)

The authors investigate the chromatic number \(\chi\) and the circular chromatic number \(\chi_c\) of the Cartesian sum \(G\oplus H\) of two graphs \(G\) and \(H\). They prove that \[ \chi(G\oplus H)\leq \max\left(\lceil\chi_c(G)\chi(H)\rceil, \lceil\chi_c(H)\chi(G)\rceil\right) \] holds in general and that \[ \chi_c(G\oplus H)\leq \chi_c(G)\chi(H) \] holds under specific assumptions for the values of \(\chi_c(G)\) and \(\chi_c(H)\).