Large Rainbow Matchings in Edge-Colored Graphs with Given Average Color Degree
نویسندگان
چکیده
A rainbow matching in an edge-colored graph is a which no two edges have the same color. The color degree of vertex v number distinct colors on incident to v. Kritschgau [Electron. J. Combin. 27(3), 2020] studied existence matchings G with average at least 2k, and proved some sufficient conditions for marching size k G. include that $$|V(G)|\ge 12k^2+4k$$ , or properly 8k$$ . In this paper, we show every 4k-4$$ $$2k-1$$ contains k. addition, also prove strongly bound sharp complete graphs.
منابع مشابه
Large Rainbow Matchings in Edge-Colored Graphs
A rainbow subgraph of an edge-colored graph is a subgraph whose edges have distinct colors. The color degree of a vertex v is the number of different colors on edges incident with v. Wang and Li conjectured that for k ≥ 4, every edge-colored graph with minimum color degree k contains a rainbow matching of size at least dk/2e. A properly edge-colored K4 has no such matching, which motivates the ...
متن کاملRainbow Matchings in Properly Edge Colored Graphs
Let G be a properly edge colored graph. A rainbow matching of G is a matching in which no two edges have the same color. Let δ denote the minimum degree of G. We show that if |V (G)| ≥ 8δ 5 , then G has a rainbow matching of size at least ⌊ 5 ⌋. We also prove that if G is a properly colored triangle-free graph, then G has a rainbow matching of size at least ⌊ 3 ⌋.
متن کاملRainbow Path and Color Degree in Edge Colored Graphs
Let G be an edge colored graph. A rainbow path in G is a path in which all the edges are colored with distinct colors. Let dc(v) be the color degree of a vertex v in G, i.e. the number of distinct colors present on the edges incident on the vertex v. Let t be the maximum length of a rainbow path in G. Chen and Li (2005) showed that if dc > k (k > 8), for every vertex v of G, then t > ⌈ 3k 5 ⌉ +...
متن کاملColor Degree Condition for Large Heterochromatic Matchings in Edge-Colored Bipartite Graphs
Let G = (V,E) be an edge-colored graph, i.e., G is assigned a surjective function C : E → {1, 2, · · · , r}, the set of colors. A matching of G is called heterochromatic if its any two edges have different colors. Let (B,C) be an edge-colored bipartite graph and d(v) be color degree of a vertex v. We show that if d(v) ≥ k for every vertex v of B, then B has a heterochromatic matching of cardina...
متن کاملLarge Rainbow Matchings in Edge-Coloured Graphs
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 . A properly edge-coloured K4 has no such matching, which motivates ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Graphs and Combinatorics
سال: 2022
ISSN: ['1435-5914', '0911-0119']
DOI: https://doi.org/10.1007/s00373-022-02551-6