2015/05/17 by Noga Alon, Alon, Noga, Humberto Naves +3 · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Biological sciences #FOS: Computer and information sciences #FOS: Mathematics #Plant biochemistry and biosynthesis #Populations and Evolution (q-bio.PE) #Traditional and Medicinal Uses of Annonaceae #cs.DM #math.CO #q-bio.PE
paper · pdf · doi:10.48550/arxiv.1505.04344
arXiv admin note: text overlap with arXiv:1203.2723
openalex publication_date 2015/05/17 · arxiv created 2016/02/03 · arxiv updated 2016/02/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
A conjecture of Bandelt and Dress states that the maximum quartet distance between any two phylogenetic trees on n leaves is at most (\frac 23 +o(1))\binomn4. Using the machinery of flag algebras we improve the currently known bounds regarding this conjecture, in particular we show that the maximum is at most (0.69 +o(1))\binomn4. We also give further evidence that the conjecture is true by proving that the maximum distance between caterpillar trees is at most (\frac 23 +o(1))\binomn4.