@LuckyChouhan My favorite concepts in Combinatorics are, in no particular order, Dilworth theorem (Hall's theorem), Vizing's theorem in edge coloring, Brooks theorem in vertex coloring, 4 and 5 color theorem of planar graphs, Spectra of Laplacian and Adjacency matrices of graphs/matroids, Sperner lemma, Lovasz local lemma, Lovasz proof of Kneser conjecture, and the master Combinatorial Nullstellensatz and it's corollary Alon-Tarsi theorem