22 papers
A human-checkable proof of the 112-vertex counterexample to the Petersen coloring conjecture
Jorik Jooken
The Petersen coloring conjecture of Jaeger asserts that every bridgeless cubic graph admits a Petersen coloring. Recently, Putman presented an explicit counterexample on vert…
On the order-diameter ratio of girth-diameter cages
Stijn Cambie, Jan Goedgebeur, Jorik Jooken +1
For integers , a -cage (or simply girth-diameter cage) is a smallest -regular graph of girth and diameter (if it exists). The order of a -cage i…
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…
The Gray graph is pseudo 2-factor isomorphic
Marien Abreu, Jan Goedgebeur, Jorik Jooken +2
A graph is pseudo 2-factor isomorphic if all of its 2-factors have the same parity of number of cycles. Abreu et al. [J. Comb. Theory, Ser. B. 98 (2008) 432--442] conjectured that…