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dc.contributor.authorDalfó, Cristina
dc.contributor.authorFiol, Miguel Angel
dc.description.abstractA 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.ca_ES
dc.description.sponsorshipThis research has been partially supported by the Agency for Management of Universities and Research Grants of Catalonia (AGAUR) under the project 2017SGR1087. The first author has also received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 734922.ca_ES
dc.publisherFaculty of Mathematics and Natural Sciencesca_ES
dc.publisherInstitut Teknologi Bandung (ITB) Indonesiaca_ES
dc.publisherIndonesian Combinatorial Society (InaCombS)ca_ES
dc.publisherGTA Research GroupGTA Research Groupca_ES
dc.relation.isformatofReproducció del document publicat a
dc.relation.ispartofThe Electronic Journal of Graph Theory and Applications, 2018, vol. 6, núm. 2, p. 282-305ca_ES
dc.rightscc-by-sa (c) Cristina Dalfo et al., 2018ca_ES
dc.subjectBoolean algebraca_ES
dc.subjectRamsey theoryca_ES
dc.titleGraphs, friends and acquaintancesca_ES

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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