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Gallai–Ramsey Numbers Involving a Rainbow 4-Path
Graphs and Combinatorics, 2023 Given two non-empty graphs $G,H$ and a positive integer $k$, the Gallai-Ramsey number $\operatorname{gr}_k(G:H)$ is defined as the minimum integer $N$ such that for all $n\geq N$, every $k$-edge-coloring of $K_n$ contains either a rainbow colored copy of $G$ or a monochromatic copy of $H$.
Jinyu Zou +3 more
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Rainbow cycles vs. rainbow paths
, 2020 An edge-colored graph $F$ is {\it rainbow} if each edge of $F$ has a unique color. The {\it rainbow Turán number} $\mathrm{ex}^*(n,F)$ of a graph $F$ is the maximum possible number of edges in a properly edge-colored $n$-vertex graph with no rainbow copy of $F$.
Halfpap, Anastasia, Palmer, Cory
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Desimal, 2021 A graph is said rainbow connected if no path has more than one vertices of the same color inside. The minimum number of colors required to make a graph to be rainbow vertex-connected is called rainbow vertex connection-number and denoted by rvc(G ...
Afifah Farhanah Akadji +3 more
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Total Rainbow Connection Number of Some Graph Operations
Axioms, 2022 In a graph H with a total coloring, a path Q is a total rainbow if all elements in V(Q)∪E(Q), except for its end vertices, are assigned different colors. The total coloring of a graph H is a total rainbow connected coloring if, for any x,y∈V(H), there is
Hengzhe Li, Yingbin Ma, Yan Zhao
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CoRR, 2012 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 K_n, there is a rainbow path on (3/4-o(1))n vertices, improving on the previously best bound of (2n+1)/3 from ...
Heidi Gebauer, Frank Mousset
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Rainbow Path and Color Degree in Edge Colored Graphs [PDF]
The Electronic Journal of Combinatorics, 2014 Let $G$ be an edge colored graph. A rainbow pathin $G$ is a path in which all the edges are colored with distinct colors. Let $d^c(v)$ 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 $G$.
Anita Das 0001 +2 more
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Rainbow connection number of comb product of graphs
Electronic Journal of Graph Theory and Applications, 2022 An edge-colored graph G is called a rainbow connected if any two vertices are connected by a path whose edges have distinct colors. Such a path is called a rainbow path.
Dinny Fitriani +2 more
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Hardness Results for Total Rainbow Connection of Graphs
Discussiones Mathematicae Graph Theory, 2016 A total-colored path is total rainbow if both its edges and internal vertices have distinct colors. The total rainbow connection number of a connected graph G, denoted by trc(G), is the smallest number of colors that are needed in a total-coloring of G ...
Chen Lily, Huo Bofeng, Ma Yingbin
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THE RAINBOW VERTEX-CONNECTION NUMBERS OF WHEEL-SHIELD GRAPHS
BarekengLet be a nontrivial simple connected graph, be an edge of and be an integer greater than or equal to . A path of order , denoted by , is a graph whose vertices can be labelled such that .
Ratnaning Palupi, A. N. M. Salman
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Proceedings of the AAAI Conference on Artificial IntelligenceWe introduce the algorithmic problem of finding a locally rainbow path of length l connecting two distinguished vertices s and t in a vertex-colored directed graph. Herein, a path is locally rainbow if between any two visits of equally colored vertices, the path traverses consecutively at leaset r differently colored vertices.
Till Fluschnik +2 more
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