WebMay 1, 2024 · Here, we consider degree conditions on ensuring the existence of rainbow cycles of fixed length . To that end, a vertex in an edge-colored graph has - degree given by the number of distinct colors assigned by to the edges . We set for the minimum -degree in . The following result of H. Li [10] motivates our current work. Theorem 1.1 WebJul 10, 2024 · A rainbow cycle is a cycle with all its edges of different colors. Single vertices are considered trivial rainbow cycles. A rainbow cover for the graph Gis defined as a disjoint collection of rainbow cycles, which means that each vertex can …
Note on Rainbow Triangles in Edge-Colored Graphs
WebFeb 2, 2012 · A rainbow subgraph of an edge-coloured graph is a subgraph whose edges have distinct colours. The colour degree of a vertex v is the number of different colours on edges incident with v. Wang and Li conjectured that for k ≥ 4, every edge-coloured graph with minimum colour degree k contains a rainbow matching of size at least ⌈ k /2⌉. WebA rainbow subgraph of an edge-colored graph has all edges of distinct colors. A random d-regular graph with d even, and having edges colored randomly with d/2 of each of n colors, has a rainbow Hamilton cycle with probability tending to 1 as n →∞, for fixed ... crystal shops iowa city
Rainbow Triangles in Arc-Colored Tournaments SpringerLink
WebOct 21, 2024 · Note on rainbow cycles in edge-colored graphs Xiaozheng Chen, Xueliang Li Let be a graph of order with an edge-coloring , and let denote the minimum color degree … WebAbstract. An edge coloring of a simple graph G is said to be proper rainbow-cycle-forbidding (PRCF, for short) if no two incident edges receive the same color and for any cycle in G, at least two edges of that cycle receive the same color. A graph G is defined to be PRCF-good if it admits a PRCF edge coloring, and G is deemed PRCF-bad otherwise. Webwhere each color class forms a perfect (if n is even) or nearly perfect (if n is odd) matching. A colored subgraph of Kn is called rainbow if its edges have different colors. The size of rainbow subgraphs of maximum degree two, i.e. union of paths and cycles in proper colorings, has been well investigated. A consequence of Ryser’s crystal shops kamloops