2018/03/19 by Pei Wu, Wu, Pei
Computer Science · #Advanced Graph Theory Research #Combinatorics (math.CO) #Complexity and Algorithms in Graphs #FOS: Mathematics #Optimization and Search Problems
paper · pdf · doi:10.48550/arxiv.1803.06825
openalex publication_date 2018/03/19 · openalex created_date 2018/03/29 · openalex updated_date 2026/07/28
The Las Vergnas' strong map conjecture, states that any strong map of oriented matroids f:M1\rightarrowM2 can be factored into extensions and contractions. The conjecture is known to be false due to a construction by Richter-Gebert, he find a non-factorizable strong map f:M1\rightarrowM2, however in his example M1 is not realizable. The problem that whether there exists a non-factorizable strong map between realizable oriented matroids still remains open. In this paper we provide a counterexample to the strong map conjecture on realizable oriented matroids, which is a strong map f:M1\rightarrowM2, M1 is an alternating oriented matroid of rank 4 and f has corank 2. We prove it is not factorizable by showing that there is no uniform oriented matroid M′ of rank 3 such that M1\rightarrowM′\rightarrowM2.