Comportamientos extra\~nos del infinito: Gr\'aficas Infinitas

TL;DR

This paper explores the intriguing contrasts and similarities between infinite and finite combinatorics through concrete graph theory examples, aiming to provide intuition about infinity's behavior in combinatorial mathematics.

Contribution

It presents specific examples illustrating both the similarities and radical differences between infinite and finite combinatorics within graph theory.

Findings

Examples of infinite combinatorial behaviors in graph theory.

Identification of key differences between finite and infinite cases.

Insights into the nature of infinity in combinatorial contexts.

Abstract

Infinitary Combinatorics shows interesting contrasts, with many similarities but also several important differences with its finite analog. The purpose of this paper is to present some concrete examples, both of similarities and of radical differences, in order to provide some intuition about the behaviour of infinity in the combinatorial setting. Our examples are taken from the branch of mathematics known as Graph Theory. -- La combinatoria infinita (tem\'atica que, a ra\'{\i}z del trabajo de Cantor, actualmente es posible estudiar de manera completamente formal) nos presenta un interesante contraste de semejanzas y diferencias con su an\'alogo finito. El prop\'osito de este art\'{\i}culo es presentar algunos ejemplos concretos tanto de semejanzas, como de diferencias radicales, para proporcionar cierta intuici\'on acerca del comportamiento del infinito en el \'ambito combinatorio. Nuestros ejemplos son tomados de la rama de las matem\'aticas conocida como Teor\'{\i}a de Gr\'aficas.