4 papers
Graph Puzzles III.1: A Proof of Sabidussi's Compatibility Conjecture
Nikolay Ulyanov
We prove Sabidussi's compatibility conjecture. Let be a finite connected multigraph in which every vertex has even degree and the minimum degree is at least four, and let b…
Graph Puzzles II.1: Counterexamples to Jain's Second Unit Vector Flows Conjecture
Nikolay Ulyanov
A -dimensional nowhere-zero flow on a graph is a flow where each edge is assigned a -dimensional vector with unit norm (which corresponds to the points of a -dimension…
Open problems of the 33rd Workshop on Cycles and Colourings
János Barát, Zdeněk Dvořák, Penny Haxell +6
Since its beginnings, every Cycles and Colourings workshop holds one or two open problem sessions; this document contains the problems (together with notes regarding the current st…
Graph Puzzles I.1: Oriented Berge-Fulkerson Conjecture
Nikolay Ulyanov
The Berge-Fulkerson conjecture states that every bridgeless cubic graph can be covered with six perfect matchings such that each edge is covered exactly twice. An equivalent reform…