NDLI: Monochromatic Structures in Edge-coloured Graphs and Hypergraphs-A survey

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Monochromatic Structures in Edge-coloured Graphs and Hypergraphs-A survey

Content Provider	Semantic Scholar
Author	Fujita, Shinya Liu, Henry Magnant, Colton
Copyright Year	2015
Abstract	Given a graph whose edges are coloured, on how many vertices can we find a monochromatic subgraph of a certain type, such as a connected subgraph, or a cycle, or some type of tree? Also, how many such monochromatic subgraphs do we need so that their vertex sets form either a partition or a covering of the vertices of the original graph? What happens for the analogous situations for hypergraphs? In this survey, we shall review known results and conjectures regarding these questions. In most cases, the edge-coloured (hyper)graph is either complete, or non-complete but with a density constraint such as having fixed independence number. For some problems, a restriction may be imposed on the edge-colouring, such as when it is a Gallai colouring (i.e. the edge-colouring does not contain a triangle with three distinct colours). Many examples of edge-colourings will also be presented, each one either showing the sharpness of a result, or supporting a possible conjecture. ∗Research supported by JSPS KAKENHI Grant Number 23740095. †Research partially supported by FCT Fundação para a Ciência e a Tecnologia (Portuguese Foundation for Science and Technology), through the projects PEst-OE/MAT/UI0297/2014 (Centre for Mathematics and its Applications) and PTDC/MAT/113207/2009.
File Format	PDF HTM / HTML
Alternate Webpage(s)	http://www.cantab.net/users/henry.liu/FLM%20survey.pdf
Alternate Webpage(s)	http://www.mililink.com/upload/article/813658924IJGTA%20v1i1%203-56.pdf
Language	English
Access Restriction	Open
Content Type	Text
Resource Type	Article

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