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 is defined as minimum k such that any k-edge-coloring of contains a i.e., copy all its edges have different colors. Denote by Mt matching size t Tn class plane triangulations order n, respectively. Jendrol′ et al. initiated investigate numbers matchings in triangulations. They proved some bounds values rb(Tn,Mt) also obtained exact t=2,3,4. Later, t=5 t=6 been determined Qin Chen al., 2n+3t−14≤rb(Tn,Mt)≤2n+4t−13 n≥3t−6 t≥6. In this paper, we determine large namely, rb(Tn,Mt)=2n+3t−14 n≥9t+3 t≥7.