14 citations · 66 across the 66 of their papers we have counts for
15 papers · 1 filter
Better bounds for the union-closed sets conjecture using the entropy approach
Stijn Cambie
We improve the best known constant for which the union-closed conjecture is known to be true, by using dependent samples as suggested by Sawin and the entropy…
The minimum number of maximal independent sets in twin-free graphs
Stijn Cambie, Stephan Wagner
The problem of determining the maximum number of maximal independent sets in certain graph classes dates back to a paper of Miller and Muller and a question of Erdős and Moser from…
Set systems without a simplex, Helly hypergraphs and union-efficient families
Stijn Cambie, Nika Salia
We present equivalent formulations for concepts related to set families for which every subfamily with empty intersection has a bounded sub-collection with empty intersection. Here…
The average solution of a TSP instance in a graph
Stijn Cambie
We define the average -TSP distance of a graph as the average length of a shortest walk visiting vertices, i.e. the expected length of the solution for a ran…
Trees maximizing the number of almost-perfect matchings
Stijn Cambie, Bradley McCoy, Gunjan Sharma +2
We characterize the extremal trees that maximize the number of almost-perfect matchings, which are matchings covering all but one or two vertices, and those that maximize the numbe…
On the main distance-based entropies: the eccentricity- and Wiener-entropy
Stijn Cambie, Yanni Dong
We define the Wiener-entropy, which is together with the eccentricity-entropy one of the most natural distance-based graph entropies. By deriving the (asymptotic) extremal behaviou…
Extremal and monotone behaviour of the Sudoku number and related critical set parameters
Stijn Cambie
The Sudoku number has been defined under various names, indicating it is a natural concept. There are four variants of this parameter, that can be related to the maximum and minimu…
Extremal values of degree-based entropies of bipartite graphs
Stijn Cambie, Yanni Dong, Matteo Mazzamurro
We characterize the bipartite graphs that minimize the (first-degree based) entropy, among all bipartite graphs of given size, or given size and (upper bound on the) order. The ext…
Resolution of Yan's conjecture on entropy of graphs
Stijn Cambie, Matteo Mazzamurro
The first degree-based entropy of a graph is the Shannon entropy of its degree sequence normalized by the degree sum. In this paper, we characterize the connected graphs with given…
Extremal entropy for graphs with given size
Stijn Cambie, Matteo Mazzamurro
The first degree-based entropy of a graph is the Shannon entropy of its degree sequence normalized by the degree sum. Its correct interpretation as a measure of uniformity of the d…
Optimally Reconfiguring List and Correspondence Colourings
Stijn Cambie, Wouter Cames van Batenburg, Daniel W. Cranston
The reconfiguration graph for the -colourings of a graph has a vertex for each proper -colouring of , and two vertices of are adj…
When removing an independent set is optimal for reducing the chromatic number
Stijn Cambie, John Haslegrave, Ross J. Kang
How large must the chromatic number of a graph be, in terms of the graph's maximum degree, to ensure that the most efficient way to reduce the chromatic number by removing vertices…
A proof of Frankl's conjecture on cross-union families
Stijn Cambie, Jaehoon Kim, Hong Liu +1
The families of -element subsets of are called cross-union if there is no choice of $F_0\in \mathcal F_0, \ldots, F_s\…
Maximum size of digraphs of given radius
Stijn Cambie
In , Vizing determined the maximum size of a graph with given order and radius. In , Fridman answered the same question for digraphs with given order and outradius. We…
Extremal total distance of graphs of given radius I
Stijn Cambie
In 1984, Plesník determined the minimum total distance for given order and diameter and characterized the extremal graphs and digraphs. We prove the analog for given order and radi…