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https://www.um.edu.mt/library/oar/handle/123456789/118845
Title: | The Erdős–Faber–Lovász conjecture revisited |
Authors: | Gauci, John Baptist Zerafa, Jean Paul |
Keywords: | Graph theory Graphic methods Mathematics -- Charts, diagrams, etc. |
Issue Date: | 2021 |
Publisher: | Aracne Editrice |
Citation: | Gauci, J. B., & Zerafa, J. P. (2021). The Erdős–Faber–Lovász conjecture revisited. Note di Matematica, 41(2), 1-7. |
Abstract: | The Erdős–Faber–Lovász Conjecture, posed in 1972, states that if a graph G is the union of n cliques of order n (referred to as defining n-cliques) such that two cliques can share at most one vertex, then the vertices of G can be properly coloured using n colours. Although still open after almost 50 years, it can be easily shown that the conjecture is true when every shared vertex belongs to exactly two defining n-cliques. We here provide a quick and easy algorithm to colour the vertices of G in this case, and discuss connections with clique-decompositions and edge-colourings of graphs, |
URI: | https://www.um.edu.mt/library/oar/handle/123456789/118845 |
Appears in Collections: | Scholarly Works - FacEduTEE |
Files in This Item:
File | Description | Size | Format | |
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The_Erdős–Faber–Lovász_conjecture_revisited_2021.pdf | 339.65 kB | Adobe PDF | View/Open |
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