Jorik Jooken

KU Leuven | ku leuven · Department of Computer Science

An $(\{r,m\};g)$-graph is a (simple, undirected) graph of girth $g\geq3$ with vertices of degrees $r$ and $m$ where $2 \leq r < m$ . Given $r,m,g$, we seek the $(\{r,m\};g)$-graphs of minimum order, called $(\{r,m\};g)$-cages or bi-regular cages, whose order is denoted by $n(\{r,m\};g)$. In this paper, we use computational methods for finding $(\{r...

We show that there exists an infinite family of cubic $2$-connected non-hamiltonian graphs with girth at least $5$ containing a unique longest cycle.

Conduction graphs are defined here in order to elucidate at a glance the often complicated conduction behaviour of molecular graphs as ballistic molecular conductors. The graph $G^{\mathrm C}$ describes all possible conducting devices associated with a given base graph $G$ within the context of the Source-and-Sink-Potential model of ballistic condu...

A vertex-girth-regular $vgr(v,k,g,\lambda)$-graph is a $k$-regular graph of girth $g$ and order $v$ in which every vertex belongs to exactly $\lambda$ cycles of length $g$. While all vertex-transitive graphs are necessarily vertex-girth-regular, the majority of vertex-girth-regular graphs are not vertex-transitive. Similarly, while many of the smal...

Inspired by Sheehan’s conjecture that no 4 4 -regular graph contains exactly one hamiltonian cycle, we prove results on hamiltonian cycles in regular graphs and nearly regular graphs. We fully disprove a conjecture of Haythorpe on the minimum number of hamiltonian cycles in regular hamiltonian graphs, thereby extending a result of Zamfirescu, as we...

Given two graphs \(H_1\) and \(H_2\), a graph is \((H_1,H_2)\)-free if it contains no induced subgraph isomorphic to \(H_1\) nor \(H_2\). A dart is the graph obtained from a diamond by adding a new vertex and making it adjacent to exactly one vertex with degree 3 in the diamond. In this paper, we show that there are finitely many k-vertex-critical...

We propose a new methodology to develop heuristic algorithms using tree decompositions. Traditionally, such algorithms construct an optimal solution of the given problem instance through a dynamic programming approach. We modify this procedure by introducing a parameter W that dictates the number of dynamic programming states to consider. We drop t...

Decades of research on the 0-1 knapsack problem led to very efficient algorithms that are able to quickly solve large problem instances to optimality. This prompted researchers to also investigate whether relatively small problem instances exist that are hard for existing solvers and investigate which features characterize their hardness. Previousl...

We fully disprove a conjecture of Haythorpe on the minimum number of hamiltonian cycles in regular hamiltonian graphs, thereby extending a result of Zamfirescu, as well as correct and complement Haythorpe's computational enumerative results from [Experim. Math. 27 (2018) 426-430]. Thereafter, we use the Lov\'asz Local Lemma to extend Thomassen's in...

In this article we propose a heuristic algorithm to explore search space trees associated with instances of combinatorial optimization problems. The algorithm is based on Monte Carlo tree search, a popular algorithm in game playing that is used to explore game trees and represents the state-of-the-art algorithm for a number of games. Several enhanc...

Predicting and comparing algorithm performance on graph instances is challenging for multiple reasons. First, there is not always a standard set of instances to benchmark performance. Second, using existing graph generators results in a restricted spectrum of difficulty and the resulting graphs are not always diverse enough to draw sound conclusion...

We propose a new heuristic algorithm for the Maximum Happy Vertices problem, using tree decompositions. Traditionally, such algorithms construct an optimal solution of the given problem instance through a dynamic programming approach. We modify this procedure by integrating a parameter $W$ that dictates the number of dynamic programming states to c...

The 0-1 knapsack problem is an important optimization problem, because it arises as a special case of a wide variety of optimization problems and has been generalized in several ways. Decades of research have resulted in very powerful algorithms that can solve large knapsack problem instances involving thousands of decision variables in a short amo...

In this article, a novel approach to solve combinatorial optimization problems is proposed. This approach makes use of a heuristic algorithm to explore the search space tree of a problem instance. The algorithm is based on Monte Carlo tree search, a popular algorithm in game playing that is used to explore game trees. By leveraging the combinatoria...

Predicting and comparing algorithm performance on graph instances is challenging for multiple reasons. First, there is usually no standard set of instances to benchmark performance. Second, using existing graph generators results in a restricted spectrum of difficulty and the resulting graphs are usually not diverse enough to draw sound conclusions...

This paper proposes a local search algorithm for a specific combinatorial optimisation problem in graph theory: the Hamiltonian completion problem (HCP) on undirected graphs. In this problem, the objective is to add as few edges as possible to a given undirected graph in order to obtain a Hamiltonian graph. This problem has mainly been studied in t...

This paper proposes a local search algorithm for a specific combinatorial optimisation problem in graph theory: the Hamiltonian Completion Problem (HCP) on undirected graphs. In this problem, the objective is to add as few edges as possible to a given undirected graph in order to obtain a Hamiltonian graph. This problem has mainly been studied in t...