Graphs, friends and acquaintances

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2018
Author
Dalfó, Cristina
Fiol, Miguel Angel
Suggested citation
Dalfó, Cristina; Fiol, Miguel Angel; . (2018) . Graphs, friends and acquaintances. The Electronic Journal of Graph Theory and Applications, 2018, vol. 6, núm. 2, p. 282-305. https://doi.org/10.5614/ejgta.2018.6.2.8.
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Abstract
A graph is a mathematical object modeling the existence of a certain relation between pairs of elements of a given set. Many of the first results concerning graphs made reference to relationships between groups of people. In this article, we comment on four results of this kind: the Handshake lemma
(related to graph colorings and Boolean algebra), a lemma on known and unknown people at a cocktail party (to Ramsey theory), a theorem on friends in common (to distance-regularity and coding theory), and Hall's Marriage theorem (to the theory of networks). These four areas of graph theory, often with problems which are easy to state but difficult to solve, are extensively developed and currently give rise to much research work. As examples of representative problems and results of these areas we may cite the following: the Four Colors Theorem (4CTC), the Ramsey numbers, problems of the existence of distance-regular graphs and completely regular codes, and finally the study of topological proprieties of interconnection networks.
URI
http://hdl.handle.net/10459.1/65737
DOI
https://doi.org/10.5614/ejgta.2018.6.2.8
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The Electronic Journal of Graph Theory and Applications, 2018, vol. 6, núm. 2, p. 282-305
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cc-by-sa (c) Cristina Dalfo et al., 2018
Except where otherwise noted, this item's license is described as cc-by-sa (c) Cristina Dalfo et al., 2018