Discrete Mathematics ( IF 0.7 ) Pub Date : 2021-01-25 , DOI: 10.1016/j.disc.2021.112301 Zhongmei Qin , Yongxin Lan , Yongtang Shi , Jun Yue
Given two graphs and , the rainbow number for with respect to is defined as the minimum number such that any -edge-coloring of contains a rainbow , i.e., a copy of , all of its edges have different colors. Denote by a matching of size and the class of all plane triangulations of order , respectively. Jendrol et al. initiated to investigate the rainbow numbers for matchings in plane triangulations. They proved some bounds for the values of and also obtained the exact values for . Later, the exact values for and have been determined by Qin et al. and Chen et al., respectively. Chen et al. also proved that for all and . In this paper, we determine the exact values of for large , namely, for all and .
中文翻译:
精确的彩虹数字,用于平面三角剖分中的匹配
给定两个图 和 ,彩虹号 对于 关于 定义为最小数量 这样任何 的边缘着色 包含彩虹 ,即 ,其所有边缘都有不同的颜色。表示为 大小匹配 和 所有平面三角剖分的类别 , 分别。詹德罗等。开始研究彩虹数字以匹配平面三角剖分。他们证明了 并获得了确切的值 。稍后,确切的值 和 由秦等人确定。和Chen等人。Chen等。也证明了 对全部 和 。在本文中,我们确定的确切值 大 ,即 对全部 和 。