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Last semester i took a course in Topology, and when addressing the Tijonov theorem, our professor mentioned (and proved) the Erdös theorem about c-colorings. Also, while preparing an algebra final and consulting Dummit's book, i stumbled upon some consequences of Gröbner bases in graph colorings (also, the same applications mentioned in Loustanau's book about Gröbner bases). This results motivated me to try to introduce myself in graph theory (or at least in the basics of this field). However, i could not find a book about this field that gave an exposition about the two applications i just mentioned. So, are these two applications "exceptional", in the sense that they are more of a commentary in other fields such as topology than vital results in graph theory? In case someone knows a book about graph theory that admits the use of topology or abstract algebra, i would really appreciate it.

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  • $\begingroup$ A well-known classic is Godsil & Royle's "Algebraic Graph Theory." Perhaps this would interest you. $\endgroup$ – Paralyzed_by_Time Jun 30 at 1:42
  • $\begingroup$ Thanks for the recommendation, i'll give it a try! $\endgroup$ – Hmm Jun 30 at 5:19

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