Induced Colorful Trees and Paths in Large Chromatic Graphs
نویسندگان
چکیده
منابع مشابه
Induced Colorful Trees and Paths in Large Chromatic Graphs
In a proper vertex coloring of a graph a subgraph is colorful if its vertices are colored with different colors. It is well-known that in every proper coloring of a k-chromatic graph there is a colorful path Pk on k vertices. If the graph is k-chromatic and triangle-free then in any proper coloring there is also a path Pk which is an induced subgraph. N.R. Aravind conjectured that these results...
متن کاملColorful paths for 3-chromatic graphs
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 ...
متن کاملColorful Paths in Vertex Coloring of Graphs
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...
متن کاملOn Induced Paths, Holes and Trees in Random Graphs
We study the concentration of the largest induced paths, trees and cycles (holes) in the Erdos-Renyi random graph model and prove a 2-point concentration for the size of the largest induced path and hole, for all p = Ω(n ln n). As a corollary, we obtain an improvement over a result of Erdos and Palka concerning the size of the largest induced tree in a random graph. Further, we study the path c...
متن کاملInduced Subgraphs of Graphs with Large Chromatic Number IX: Rainbow Paths
We prove that for all integers κ, s ≥ 0 there exists c with the following property. Let G be a graph with clique number at most κ and chromatic number more than c. Then for every vertex-colouring (not necessarily optimal) of G, some induced subgraph of G is an s-vertex path, and all its vertices have different colours. This extends a recent result of Gyárfás and Sárközy [6], who proved the same...
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: The Electronic Journal of Combinatorics
سال: 2016
ISSN: 1077-8926
DOI: 10.37236/6239