#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
Thomassé's work was a breakthrough because it transitioned the #DeanConjecture from a pure existence problem to an #algorithmic one. This is crucial for practical applications and further research. #ProblemSolving #AlgorithmicThinking #Innovation #math #computerScience
The constructive nature of Thomassé's proof opens up possibilities for efficient #algorithms to find the vertex in the #DeanConjecture. This could have implications for tournament-related problems in computer science. #TCS #ComputationalComplexity #Algorithms
Thomassé's use of median orders showcases the power of combinatorial arguments in #GraphTheory. It provides a more direct and intuitive understanding of the underlying structure of tournaments. #CombinatorialMath #GraphStructure #Mathematics #DeanConjecture #SeymourConjecture #math
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
Day 11 of #SSNC facts! Let's explore Thomassé's (w/ Havet) approach to the #DeanConjecture! They introduced "median orders" in tournaments. This is as a way to arrange vertices to reveal structural properties. This is a powerful combinatorial tool! #GraphTheory #MedianOrders #Combinatorics #math
Day 10 of #SSNC facts! The #DeanConjecture states in any tournament, there's a vertex 'v' where |out-neighborhood(v, 2)| ≥ |out-neighborhood(v, 1)|. Simply put, you can reach more vertices in 2 steps than 1. Fisher provided a probabilistic proof. #GraphTheory #SeymourConjecture #math #research
Day 7 of the #SSNC facts! The #SeymourConjecture isn't the only conjecture in graph theory. There are related conjectures, like the #SullivanConjecture and the #DeanConjecture, that explore similar ideas about graph structure and neighborhoods. #GraphTheory #OpenProblems
