Proof: Every Tournament has Hamiltonian Path | Graph Theory

Published: 20 July 2021
on channel: Wrath of Math
11,001
180

We prove that every tournament graph contains a Hamiltonian path, that is a path containing every vertex of the graph. Recall a tournament is a directed graph with exactly one arc between each pair of vertices. The proof will proceed by contradiction, and follow a similar format to other proofs we have seen related to Hamiltonian paths, Hamiltonian cycles, and Hamiltonian graphs. #GraphTheory

Intro to Tournaments:    • Intro to Tournament Graphs | Graph Th...  
Hamiltonian Cycles, Graphs, and Paths:    • Hamiltonian Cycles, Graphs, and Paths...  
Necessary Condition for Graphs with Hamilton Paths:    • Proof: Necessary Component Condition ...  

Graph Theory Playlist:    • Graph Theory  

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