منابع مشابه
Rainbow Paths with Prescribed Ends
It was conjectured in [S. Akbari, F. Khaghanpoor, and S. Moazzeni. Colorful paths in vertex coloring of graphs. Preprint] that, if G is a connected graph distinct from C7, then there is a χ(G)-coloring of G in which every vertex v ∈ V (G) is an initial vertex of a path P with χ(G) vertices whose colors are different. In [S. Akbari, V. Liaghat, and A. Nikzad. Colorful paths in vertex coloring of...
متن کاملOn Rainbow Cycles and Paths
In a properly edge colored graph, a subgraph using every color at most once is called rainbow. In this thesis, we study rainbow cycles and paths in proper edge colorings of complete graphs, and we prove that in every proper edge coloring of Kn, there is a rainbow path on (3/4− o(1))n vertices, improving on the previously best bound of (2n + 1)/3 from [?]. Similarly, a k-rainbow path in a proper...
متن کاملOptimal Colorings with Rainbow Paths
Let G be a connected graph of chromatic number k. For a k-coloring f of G, a full f -rainbow path is a path of order k in G whose vertices are all colored differently by f . We show that G has a k-coloring f such that every vertex of G lies on a full f -rainbow path, which provides a positive answer to a question posed by Lin (Simple proofs of results on paths representing all colors in proper ...
متن کاملComplete Bipartite Graphs with No Rainbow Paths
Motivated by questions in Ramsey theory, Thomason and Wagner described the edge colorings of complete graphs that contain no rainbow path Pt of order t. In this paper, we consider the edge colorings of complete bipartite graphs that contain no rainbow path Pt. Mathematics Subject Classification: 05C15, 05C38, 05C55
متن کاملTechnical Report TR - 2008 - 021 Rainbow Paths
A k-rainbow path in a graph with colored edges is a path of length k where each edge has a different color. In this note, we settle the problem of obtaining a constructive k-coloring of the edges of Kn in which one may find, between any pair of vertices, a large number of internally disjoint krainbow paths. In fact, our construction obtains the largest possible number of paths. This problem was...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2010
ISSN: 0012-365X
DOI: 10.1016/j.disc.2009.09.010