Edge Colorings of K(m,n) with m+n-1 Colors Which Forbid Rainbow Cycles

Johnson, Peter; Zhang, Claire

doi:10.20429/tag.2017.040101

Cited by 3 publications

(22 citation statements)

References 3 publications

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“…As for the year, it was identified that the first publication was carried out in 1995 ( 17 ) , two new publications in 2001 ( 20 ) , one more in 2003 ( 21 ) and another in 2004 ( 22 ) , three publications in 2005 ( 38 ) one more was found, four in 2020 ( 43 ) and one in 2022 ( 44 ) .…”

Section: Resultsmentioning

confidence: 99%

“…The journals with the most publications on the subject were the newsletter On The Edge, with 10 publications ( 18 , 19 , 21 – 23 , 26 , 28 – 30 , 32 ) ; the Journal of Forensic Nursing, with three publications ( 24 , 34 , 40 ) and two publications in the Journal of Psychosocial Nursing and Mental Health ( 17 , 27 ) ( Chart 2 ).…”

Section: Resultsmentioning

confidence: 99%

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Forensic Nursing competencies in disasters situations: scoping review

Silva,

Haberland,

Kneodler

et al. 2023

Rev. esc. enferm. USP

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Objective: To map sources of technical-scientific information on Forensic Nursing competencies in disasters situations. Method: Scoping review developed in accordance with the JBI methodology, carried out in three stages by two reviewers independently on selected databases and gray literature, using keywords and descriptors. After reading them in full, we proceeded with data extraction and content analysis of 28 publications. Results: Identified 24 publications in English, 20 of which were produced in the United States of America. 24 competencies of forensic nurses in disasters situations were mapped, including: training; resource management; link with the justice service; direct care; psycho-emotional care; collection and preservation of traces; registration and documentation with photography; body management; maintenance of the chain of custody; and epidemiological surveillance. Conclusion: The forensic nurse acts in all phases of disasters with the affected people, families and communities, under an interdisciplinary perspective. The development of competencies aimed at the practice of Forensic Nursing in disasters should be incorporated into the training strategies of these professionals, in order to obtain better response standards.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Forensic Nursing competencies in disasters situations: scoping review

Silva,

Haberland,

Kneodler

et al. 2023

Rev. esc. enferm. USP

View full text Add to dashboard Cite

show abstract

“…We note here that JL-colorings of graphs only exist for connected graphs so this proposition implies that both A and Ā are connected and that the cut contains at least one edge, but further that the cut is an entire color class and that ϕ| A and ϕ| Ā have disjoint color sets. This was originally proved for complete graphs in [6], complete bipartite graphs in [11], and finally for complete multipartite graphs in [12]. Recently, it has been established for arbitrary JL-colored graphs in [8].…”

Section: The Structure Of Jl-coloringsmentioning

confidence: 97%

“…Recall that a JL-coloring ϕ is a rainbow cycle free (n − 1)-edge-coloring of a graph G with order n. There is a representation of JL-colorings as labeled binary trees which we will use to count RST's in a given JL-colored graph. The key to this approach, which has appeared in a series of papers of Johnson and collaborators (see [6,8,11,12]), is the following proposition: Proposition 1. Suppose ϕ is a JL-coloring of a connected graph G. Then there is a partition of V (G) into sets A and Ā, so that e(A, Ā), the set of edges between vertices in A and Ā, is monochromatic in ϕ, and both ϕ| A and ϕ| Ā are JL-colorings of the graphs induced on A and Ā respectively.…”

Section: The Structure Of Jl-coloringsmentioning

confidence: 99%

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An Extremal Problem on Rainbow Spanning Trees in Graphs

DeVilbiss

Fain

Holmes

et al. 2020

Preprint

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A spanning tree of an edge-colored graph is rainbow provided that each of its edges receives a distinct color. In this paper we consider the natural extremal problem of maximizing and minimizing the number of rainbow spanning trees in a graph G. Such a question clearly needs restrictions on the colorings to be meaningful. For edge-colorings using n − 1 colors and without rainbow cycles, known in the literature as JL-colorings, there turns out to be a particularly nice way of counting the rainbow spanning trees and we solve this problem completely for JL-colored complete graphs K n and complete bipartite graphs K n,m . In both cases, we find tight upper and lower bounds; the lower bound for K n , in particular, proves to have an unexpectedly chaotic and interesting behavior. We further investigate this question for JL-colorings of general graphs and prove several results including characterizing graphs which have JL-colorings achieving the lowest possible number of rainbow spanning trees. We establish other results for general n − 1 colorings, including providing an analogue of Kirchoff's matrix tree theorem which yields a way of counting rainbow spanning trees in a general graph G.

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ChessY: A Mathematica toolbox for the generation, visualization and analysis of positional chess graphs

Rudolph-Lilith

2019

SoftwareX

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Edge Colorings of K(m,n) with m+n-1 Colors Which Forbid Rainbow Cycles

Cited by 3 publications

References 3 publications

Forensic Nursing competencies in disasters situations: scoping review

Forensic Nursing competencies in disasters situations: scoping review

An Extremal Problem on Rainbow Spanning Trees in Graphs

ChessY: A Mathematica toolbox for the generation, visualization and analysis of positional chess graphs

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