Rainbow connection in graphs

Chartrand, Gary; Johns, Garry L.; McKeon, Kathleen A.; Zhang, Ping

doi:10.21136/mb.2008.133947

Cited by 494 publications

(367 citation statements)

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“…The concept of rainbow connection number and strong rainbow connection number was introduced and researched by Chartrand et al in [6]. An edge-coloring of a connected graph G = (V (G), E(G)) is a mapping c: E(G) → {1, 2, .…”

Section: Introductionmentioning

confidence: 99%

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(Strong) Proper Connection in Some Digraphs

Nie

2019

IEEE Access

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An arc-colored digraph D is proper connected if any pair of vertices v i , v j ∈ V (D) there is a proper v i − v j path whose adjacent arcs have different colors and a proper v j − v i path whose adjacent arcs have different colors. The proper connection number of a digraph D is the minimum number of colors needed to make D proper connected, denoted by − → pc(D). An arc-colored digraph D is strong proper connected if any pair of vertices v i , v j ∈ V (D) there is a proper v i − v j geodesic and a proper v j − v i geodesic. The strong proper connection number of D is the minimum number of colors required to color the arcs of D in order to make D strong proper connected, denoted by − → spc(D). In this paper, we will show some results on − → pc(D) and − → spc(D), mostly for the case of the (strong) proper connection numbers of cacti and circulant digraphs. INDEX TERMS Proper path, proper connection number, proper geodesic, strong proper connection number.

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Section: Introductionmentioning

confidence: 99%

“…resolved, see [5], [6], [11], [12], [15], [26], [29] for example. In the same way, Krivelevich and Yuster [14] introduced the concept of rainbow vertex connection number.…”

Section: Introductionmentioning

confidence: 99%

(Strong) Proper Connection in Some Digraphs

Nie

2019

IEEE Access

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“… Similarily we define the colour consistent outdegree as The problem of guided assembly can then be modelled as finding a rainbow path in the coloured overlap graph. A rainbow path is a path such that no two vertices have the same colour [ 21 ]. We use a modified variant of rainbow paths; we allow paths to reuse a colour in consecutive vertices and we require the colours of a path to be consecutive and increasing.…”

Section: Definitionsmentioning

confidence: 99%

Kermit: linkage map guided long read assembly

Walve

Rastas

Salmela

2019

Algorithms Mol Biol

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Background With long reads getting even longer and cheaper, large scale sequencing projects can be accomplished without short reads at an affordable cost. Due to the high error rates and less mature tools, de novo assembly of long reads is still challenging and often results in a large collection of contigs. Dense linkage maps are collections of markers whose location on the genome is approximately known. Therefore they provide long range information that has the potential to greatly aid in de novo assembly. Previously linkage maps have been used to detect misassemblies and to manually order contigs. However, no fully automated tools exist to incorporate linkage maps in assembly but instead large amounts of manual labour is needed to order the contigs into chromosomes.Results We formulate the genome assembly problem in the presence of linkage maps and present the first method for guided genome assembly using linkage maps. Our method is based on an additional cleaning step added to the assembly. We show that it can simplify the underlying assembly graph, resulting in more contiguous assemblies and reducing the amount of misassemblies when compared to de novo assembly.Conclusions We present the first method to integrate linkage maps directly into genome assembly. With a modest increase in runtime, our method improves contiguity and correctness of genome assembly.

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“…Salah satu topiknya yaitu bilangan terhubung pelangi. Bilangan terhubung pelangi pertama kali diperkenalkan oleh seorang matematikawan bernama Chartrand pada tahun 2008 [3]. Pada tahun 2009, topik bilangan terhubung pelangi ini kemudian dikembangkan oleh Krivelevich dan Yuster [4] yang memperkenalkan bilangan terhubung titik pelangi yang merupakan bilangan terkecil yang dapat membuat sebuah graf memiliki lintasan pelangi pada setiap pasang titiknya.…”

Section: Pendahuluanunclassified

Bilangan Terhubung Titik Pelangi Pada Amalgamasi Graf Berlian

Akadji

Taha

Lakisa

et al. 2019

Euler J. Ilm. Mat. Sains dan Teknol.

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Suppose there is a simple, and finite graph G = (V, E). The coloring of vertices c is denoted by c: E(G) → {1,2, ..., k} with k is the number of rainbow colors on graph G. A graph is said to be rainbow connected if every pair of points x and y has a rainbow path. A path is said to be a rainbow if there are not two edges that have the same color in one path. The rainbow connected number of graph G denoted by rc(G) is the smallest positive integer-k which makes graph G has rainbow coloring. Furthermore, a graph is said to be connected to rainbow vertex if at each pair of vertices x and y there are not two vertices that have the same color in one path. The rainbow vertex connected to the number of graph G is denoted by rvc(G) is the smallest positive integer-k which makes graph G has rainbow coloring. This paper discusses rainbow vertex-connected numbers in the amalgamation of a diamond graph. A diamond graph with 2n points is denoted by an amalgamation of a diamond graph by adding the multiplication of the graph t at point v is denoted by Amal (Brn,v,t).

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Rainbow connection in graphs

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Cited by 494 publications

References 0 publications

(Strong) Proper Connection in Some Digraphs

(Strong) Proper Connection in Some Digraphs

Kermit: linkage map guided long read assembly

Bilangan Terhubung Titik Pelangi Pada Amalgamasi Graf Berlian

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