#Challenge! 🧠 Given the attached #OrientedGraph, what node order maximizes the number of forward edges? (Median Order!) Havet & Thomassé used this concept in their work. Show your solution! #GraphTheory #MedianOrder #Algorithms #TournamentTheory #DeanConjecture #SeymourConjecture #math #mathematics

A crucial part of Fisher's argument involved setting up inequalities related to the sizes of out-neighborhoods. By carefully defining a probability distribution, he showed those inequalities held on average. This demonstrated the existence of that vertex. #Inequalities #TournamentTheory

Unlike Fisher's probabilistic existence proof, Thomassé's method is constructive, #algorithmic. It provides a way to find the vertex satisfying the #DeanConjecture. This is a game-changer for applications! #Algorithms #ConstructiveProof #TournamentTheory #SeymourConjecture

Median orders have become a powerful tool in #TournamentTheory, thanks to Havet and Thomassé. It provided new insights into the structure of tournaments and paved the way for solving other related problems. #GraphTheory #GraphAnalysis #MathematicalTools #Algorithms