Exact Rainbow Numbers For Matchings In Plane Triangulations

Given two graphs G and H, the rainbow number rb(G, H) for H with respect to G is defined as the minimum number k such that any k-edge-coloring of G contains a rainbow H, i.e., a copy of H, all of its edges have different colors. Denote by Mt a matching of size t and T-n the class of all plane triangulations of order n, respectively. Jendrol' et al. initiated to investigate the rainbow numbers for matchings in plane triangulations. They proved some bounds for the values of rb(T-n, M-t) and also obtained the exact values for t = 2, 3, 4. Later, the exact values for t = 5 and t = 6 have been determined by Qin et al. and Chen et al., respectively. Chen et al. also proved that 2n + 3t - 14 <= rb(T-n, M-t) <= 2n + 4t - 13 for all n >= 3t - 6 and t >= 6. In this paper, we determine the exact values of rb(T-n, M-t) for large n, namely, rb(T-n, M-t) = 2n + 3t - 14 for all n >= 9t + 3 and t >= 7. (C) 2021 Elsevier B.V. All rights reserved.