189 citations · 506 across the 54 of their papers we have counts for
8 papers · 1 filter
Structural and computational results on platypus graphs
Jan Goedgebeur, Addie Neyt, Carol T. Zamfirescu
A platypus graph is a non-hamiltonian graph for which every vertex-deleted subgraph is traceable. They are closely related to families of graphs satisfying interesting conditions r…
Smallest snarks with oddness 4 and cyclic connectivity 4 have order 44
Jan Goedgebeur, Edita Máčajová, Martin Škoviera
The family of snarks -- connected bridgeless cubic graphs that cannot be 3-edge-coloured -- is well-known as a potential source of counterexamples to several important and long-sta…
On the smallest snarks with oddness 4 and connectivity 2
Jan Goedgebeur
A snark is a bridgeless cubic graph which is not 3-edge-colourable. The oddness of a bridgeless cubic graph is the minimum number of odd components in any 2-factor of the graph. Lu…
Generation and properties of nut graphs
Kris Coolsaet, Patrick W. Fowler, Jan Goedgebeur
A nut graph is a graph on at least 2 vertices whose adjacency matrix has nullity 1 and for which non-trivial kernel vectors do not contain a zero. Chemical graphs are connected, wi…
A note on 2--bisections of claw--free cubic graphs
M. Abreu, J. Goedgebeur, D. Labbate +1
A \emph{--bisection} of a bridgeless cubic graph is a --colouring of its vertex set such that the colour classes have the same cardinality and all connected components in…
On minimal triangle-free 6-chromatic graphs
Jan Goedgebeur
A graph with chromatic number is called -chromatic. Using computational methods, we show that the smallest triangle-free 6-chromatic graphs have at least 32 and at most 40 v…