20 papers
Resolution of two conjectures by ErdÅs and Hall concerning separable numbers
Stijn Cambie, Wouter van Doorn
ErdÅs and Hall defined a pair of positive integers to be interlocking, if between any pair of consecutive divisors (both larger than ) of (resp. ) there is a di…
Fractional list packing for layered graphs
Stijn Cambie, Wouter Cames van Batenburg
The fractional list packing number of a graph is a graph invariant that has recently arisen from the study of disjoint list-colourings. It measures how…
Partitions of planar (oriented) graphs into a connected acyclic and an independent set
Stijn Cambie, François Dross, Kolja Knauer +2
A question at the intersection of Barnette's Hamiltonicity and Neumann-Lara's dicoloring conjecture is: Can every Eulerian oriented planar graph be vertex-partitioned into two acyc…
On edge-colouring-games by ErdÅs, and Bensmail and Mc Inerney
Stijn Cambie, Michiel Provoost
We study two games proposed by ErdÅs, and one game by Bensmail and Mc Inerney, all sharing a common setup: two players alternately colour edges of a complete graph, or in the bias…
On the extrema of the mean subtree order of graphs
Stijn Cambie, Jorik Jooken, Stephan Wagner
It has been conjectured that the minimum and maximum of the mean subtree order among connected graphs of order are attained by the path and clique , respectively. Ex…
Proving it is impossible; on Erdős problem
Stijn Cambie
Erdős and Graham asked for the minimum density missed by one chosen residue class for each of a prescribed collection of moduli. We give exact expressions for natural structured fa…