Rainbow numbers for matchings in plane triangulations

Improved bounds for rainbow numbers of matchings in plane triangulations

“…In this paper, we improve the upper bounds and prove that rb(T n , kK 2 ) ≤ 2n + 6k − 16 for n ≥ 2k and k ≥ 5. Especially, we show that rb(T n , 5K 2 ) = 2n + 1 for n ≥ 11 by using the method of Jendrol ′ , Schiermeyer and Tu [10]. Theorem 1.2 For n ≥ 2k and k ≥ 5, rb(T n , kK 2 ) ≤ 2n + 6k − 16.…”

“…Lemma 1.5 Let G be a planar triangulation on n ≥ 4 vertices. Then (a) ( [16,10]) for 5 ≤ n ≤ 7, G is hypoHamiltonian.…”

Anti-Ramsey problems in the generalized Petersen graphs for cycles

“…Since then, plentiful results were researched for a variety of graphs H, including cycles [1,2,12,13,18,19], cliques [4,17], trees [9,11], and matchings [7,16]. Some other graphs were also considered as the host graphs in anti-Ramsey problems, such as hypergraphs [6], hypecubes [3], complete split graphs [5,14], and triangulations [8,10,15].…”

Anti-Ramsey Numbers in Complete k-Partite Graphs

“…e anti-Ramsey problems for rainbow matchings, cycles, and trees in complete bipartite graphs have been studied in [9][10][11]. Some other graphs were also considered as the host graphs in anti-Ramsey problems, such as hypergraphs [12], hypecubes [13], plane triangulations [14], and planar graphs [15].…”