Rainbow numbers for paths in planar graphs
WebMay 19, 2014 · In the article, the existence of rainbow cycles in edge colored plane triangulations is studied. It is shown that the minimum number of colors that force the existence of a rainbow C3 in any n -vertex plane triangulation is equal to . For a lower bound and for an upper bound of the number is determined. Citing Literature Volume 78, Issue 4 WebIn graph theory, a path in an edge-colored graph is said to be rainbow if no color repeats on it. A graph is said to be rainbow-connected (or rainbow colored) if there is a rainbow path …
Rainbow numbers for paths in planar graphs
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WebA subdivision of a graph is a graph formed by subdividing its edges into paths of one or more edges. Kuratowski's theorem states that a finite graph G {\displaystyle G} is planar if it is not possible to subdivide the edges of K 5 {\displaystyle K_{5}} or K 3 , 3 {\displaystyle K_{3,3}} , and then possibly add additional edges and vertices, to ... WebJun 30, 2024 · The outer-independent 2-rainbow domination number of G, denoted by , is the minimum weight among all outer-independent 2-rainbow dominating functions f on G. In this note, we obtain new results on the previous domination parameter. Some of our results are tight bounds which improve the well-known bounds , where denotes the vertex cover …
WebOct 1, 2024 · Jendrol et al. initiated the rainbow number of matchings in planar graphs and they obtained bounds for the rainbow number of the matching k K 2 in the plane triangulations, where the gap between the lower and upper bounds is O ( k 3 ). In this paper, we show that the rainbow number of the matching k K 2 in maximal outerplanar graphs of … WebOct 16, 2012 · We begin with an introduction, and then try to organize the work into five categories, including (strong) rainbow connection number, rainbow k -connectivity, k -rainbow index, rainbow vertex-connection number, algorithms and computational complexity. This survey also contains some conjectures, open problems and questions.
WebDec 3, 2014 · Chartrand et al. computed the precise rainbow connection numbers of several graph classes including complete multipartite graphs (). The rainbow connection number … WebMay 1, 2024 · Rainbow numbers for paths in planar graphs May 2024 Applied Mathematics and Computation397(1):125918 DOI:10.1016/j.amc.2024.125918 Authors: Zhongmei Qin …
WebThis paper surveys results about planar Turán number and planar anti-Ramsey number of graphs. The goal is to give a unified and comprehensive presentation of the major results, as well as...
WebJan 1, 2014 · The study of planar anti-Ramsey numbers ar P (n, H) was initiated by Horňák, Jendrol ′ , Schiermeyer and Soták [6] (under the name of rainbow numbers). We summarize their results in [6]as... fo 76 thistleWebApr 15, 2024 · In this paper, we study the rainbow number for small graphs in planar graphs. Let C 3 +, K 1, 4 + and B denote the triangle with a pendant edge, with two pendant edges incident to a single vertex of the triangle and with two disjoint pendant edges, respectively. greenwich bmw serviceWeb(With L. Lu) On the size of planar graphs with positive Lin-Lu-Yau Ricci curvature. (With L. Lu) A note on 1-guardable graphs in the cops and robber game. Submitted. Publications (With X. Liu and X. Yu) Counting Hamiltonian cycles in planar triangulations, J. Combin. Theory Ser. B, 155 (2024), 256-277. greenwich board of ed bidsWebApr 1, 2024 · Rainbow numbers for paths in planar graphs Article May 2024 APPL MATH COMPUT Zhongmei Qin Shasha Li Yongxin Lan Jun Yue View Show abstract October … fo76 trick or treatergreenwich bmw certified pre ownedWebcycle. Thus, the number of edges which are on this cycle is at least 3 and hence the path is not rainbow. Since W n is a maximal planar graph, we have ex∗ P(n,P k) = 3n−6. Now let n … greenwich bmw pre ownedWebJan 25, 2024 · On the rainbow planar Turán number of paths Ervin Győri, Ryan R. Martin, Addisu Paulos, Casey Tompkins, Kitti Varga An edge-colored graph is said to contain a … fo76 two shot flamer