[HTML][HTML] Rainbow paths

D Dellamonica Jr, C Magnant, DM Martin - Discrete mathematics, 2010 - Elsevier
… A k -rainbow path in a graph with colored edges is a path of length k where each edge has
… k -rainbow paths. In fact, our construction obtains the largest possible number of paths. This …

On rainbow cycles and paths

H Gebauer, F Mousset - arXiv preprint arXiv:1207.0840, 2012 - arxiv.org
… Generalizing the notion of a rainbow path, we consider paths in Kn that use every color at …
such paths k-rainbow paths, where k is the number of times a color may appear on the path. …

[HTML][HTML] On finding rainbow and colorful paths

Ł Kowalik, J Lauri - Theoretical Computer Science, 2016 - Elsevier
… space algorithm for Colorful Path, our algorithm for finding rainbow paths is deterministic. …
in G ′ , hence W 1 is rainbow. By removing cycles from W 1 we obtain a rainbow path in G. □ …

Complete graphs with no rainbow path

A Thomason, P Wagner - Journal of Graph Theory, 2007 - Wiley Online Library
… number of G; that is, forbidding rainbow 3-paths does not allow any larger colorings than …
a rainbow t-path. On the other hand, we show that it is much easier to avoid a rainbow t-path for …

The rainbow connectivity of a graph

G Chartrand, GL Johns, KA McKeon… - … An International Journal, 2009 - Wiley Online Library
… By coloring the edges of G with distinct colors, we see that every two vertices of G are
connected by l internally disjoint rainbow paths and that rck(G) is defined for every integer k with 1 …

Locally Rainbow Paths

T Fluschnik, L Kellerhals, M Renken - Proceedings of the AAAI …, 2024 - ojs.aaai.org
… We introduce the algorithmic problem of finding a locally rainbow path of length l connecting
… , a path is locally rainbow if between any two visits of equally colored vertices, the path

[PDF][PDF] Rainbow cycles versus rainbow paths.

A Halfpap, C Palmer - Australas. J Comb., 2021 - ajc.maths.uq.edu.au
… Using the fact that the minimum degree in G is at least 5, we can greedily build a rainbow
path of length 3 ending at v; moreover, since this path does not extend to a rainbow-P4, then …

Long rainbow paths and rainbow cycles in edge colored graphs–A survey

H Chen - Applied Mathematics and Computation, 2018 - Elsevier
… this survey we will consider long rainbow paths rather than all rainbow paths. … rainbow path
in edge colored graphs. Since lots of results on rainbow paths especially short rainbow paths

Rainbow cycles vs. rainbow paths

A Halfpap, C Palmer - arXiv preprint arXiv:2009.00135, 2020 - arxiv.org
… Using the fact that the minimum degree in G′ is at least 5, we can greedily build a rainbow
path of length 3 ending at v; moreover, since this path does not extend to a rainbow-P4, then …

Rainbow connection in graphs

G Chartrand, GL Johns, KA McKeon, P Zhang - Mathematica bohemica, 2008 - dml.cz
path P in G is a rainbow path if no two edges of P are colored the same. The graph G is
rainbow-connected if G contains a rainbow u − v path … coloring is the rainbow connection number …