On finding rainbow and colorful paths
نویسندگان
چکیده
منابع مشابه
On 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...
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A colorful path in a graph G is a path with χ(G) vertices whose colors are different. A vcolorful path is such a path, starting from v. Let G 6= C7 be a connected graph with maximum degree ∆(G). We show that there exists a (∆(G) + 1)-coloring of G with a v-colorful path for every v ∈ V (G). We also prove that this result is true if one replaces (∆(G) + 1) colors with 2χ(G) colors. If χ(G) = ω(G...
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In this paper, we prove that every 3-chromatic connected graph, except C7, admits a 3-vertex coloring in which every vertex is the beginning of a 3-chromatic path. It is a special case of a conjecture due to S. Akbari, F. Khaghanpoor, and S. Moazzeni, cited in [P.J. Cameron, Research problems from the BCC22, Discrete Math. 311 (2011), 1074–1083], stating that every connected graph G other than ...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2016
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2016.03.017