9 papers
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…
On the girth and connectivity of cubic graphs with a unique longest cycle
Jorik Jooken, Carol T. Zamfirescu
We show that there exists an infinite family of cubic -connected non-hamiltonian graphs with girth containing a unique longest cycle.
Counting Small Cycle Double Covers
Jorik Jooken, Ben Seamone, Carol T. Zamfirescu
A theorem due to Seyffarth states that every planar -connected -vertex graph has a cycle double cover (CDC) containing at most cycles (a "small" CDC). We extend this th…
On a conjecture of Faudree and Schelp
Jan Goedgebeur, Jorik Jooken, Michiel Provoost +1
In 1976 Faudree and Schelp conjectured that in a hamiltonian-connected graph on vertices, any two distinct vertices are connected by a path of length for every .…
HIST-Critical Graphs and Malkevitch's Conjecture
Jan Goedgebeur, Kenta Noguchi, Jarne Renders +1
In a given graph, a HIST is a spanning tree without -valent vertices. Motivated by developing a better understanding of HIST-free graphs, i.e. graphs containing no HIST, in this…