Speaker: Frédéric Chyzak，Inria，France

Title: On (3, 1)-regular graphs with one more vertex than edges

Language: English

Time & Venue: 2026.10.23 10:00-11:00 南楼N219

Abstract: Sequence A339987 of the OEIS counts (3,1)-regular graphs having one more vertex than edges by half the number of vertices. A recurrence relation satisfied by this sequence was guessed by Kauers and Koutschan in 2023. We confirm it in three ways: first, by a representation as the diagonal of a triple sum and an elaborate variant of traditional creative telescoping that makes an a posteriori validation possible; second, by a residue representation and a direct calculation by reduction-based creative telescoping; third, by a combinatorial recurrence on graph families and a calculation by differential elimination. Each of those three approaches leads to a formally complete proof and involves a computer calculation in one way or another. This is joint work with Hui Huang (Fuzhou University) and Manuel Kauers (Johannes Kepler University).