18 citations · 31 across the 33 of their papers we have counts for
6 papers · 1 filter
Counterexamples to the Albertson-Berman conjecture: minimum order, connectivity and an improved ratio bound
Wouter Cames van Batenburg, Jan Goedgebeur, Jorik Jooken
In 1979, Albertson and Berman conjectured that every planar graph contains an induced forest of order at least . This long-standing conjecture was recently disproved…
Disproving the Petersen Coloring Conjecture: Theoretical Analysis and an Infinite Family of Counterexamples
Jan Goedgebeur, Jorik Jooken, Edita Máčajová +3
In 1988, Jaeger conjectured that every bridgeless cubic graph admits a Petersen coloring; that is, a map mapping any two adjacent edges of to two adjacent e…
On the number of perfect matchings in planar graphs
Jan Goedgebeur, Jorik Jooken, Tibo Van den Eede +1
We investigate the minimum non-zero number of perfect matchings in planar graphs. We prove that this is a constant for 2-connected planar graphs of minimum degree 3 and 3-connected…
Counting Hamiltonian paths between prescribed vertices in traceable graphs with a forbidden induced subgraph
Jorik Jooken, Carol T. Zamfirescu
For graphs and , we say that is -free if does not occur as an induced subgraph of . This paper is concerned with the following question: Given an -free grap…
Vertex-critical -free and -free graphs
Jorik Jooken
For graphs and , we say that is -free if neither nor is an induced subgraph of . We say that is -vertex-critical if the chromatic…
A non-existence result for vertex-girth-regular graphs
Jorik Jooken, Denys Lohvynov
A -regular graph of girth is called vertex-girth-regular if every vertex is contained in the same number of cycles of length . For integers and , we denote s…