14 citations · 66 across the 66 of their papers we have counts for
13 papers · 1 filter
Disjoint list-colorings for planar graphs
Stijn Cambie, Wouter Cames van Batenburg, Xuding Zhu
One of Thomassen's classical results is that every planar graph of girth at least is 3-choosable. One can wonder if for a planar graph of girth sufficiently large and a …
Counterexamples to conjectures on the occupancy fraction of graphs
Stijn Cambie, Jorik Jooken
The occupancy fraction of a graph is a (normalized) measure on the size of independent sets under the hard-core model, depending on a variable (fugacity) We present a criterio…
The maximum number of connected sets in regular graphs
Stijn Cambie, Jan Goedgebeur, Jorik Jooken
We improve the best known lower bounds on the exponential behavior of the maximum of the number of connected sets, , and dominating connected sets, , for regular…
Bounding mean orders of sub--trees of -trees
Stijn Cambie, Bradley McCoy, Stephan Wagner +1
For a -tree , we prove that the maximum local mean order is attained in a -clique of degree and that it is not more than twice the global mean order. We also bound the…
Corrigendum on Wiener index, Zagreb Indices and Harary index of Eulerian graphs
Stijn Cambie
In the original article ``Wiener index of Eulerian graphs'' [Discrete Applied Mathematics Volume 162, 10 January 2014, Pages 247-250], the authors state that the Wiener index (tota…
Decreasing the mean subtree order by adding edges
Stijn Cambie, Guantao Chen, Yanli Hao +1
The mean subtree order of a given graph , denoted , is the average number of vertices in a subtree of . Let be a connected graph. Chin, Gordon, MacPhee, and Vincent…
The Erdős distinct subset sums problem in a modular setting
Stijn Cambie, Jun Gao, Younjin Kim +1
We prove the following variant of the Erdős distinct subset sums problem. Given and sufficiently large , every -element set whose subset sums are distinct modul…
A precise condition for independent transversals in bipartite covers
Stijn Cambie, Penny Haxell, Ross J. Kang +1
Given a bipartite graph in which any vertex in (resp.~) has degree at most (resp.~), suppose there is a partition of that is a refin…
Progress on the union-closed conjecture and offsprings in winter 2022-2023
Stijn Cambie
Mathematicians had little idea whether the easy-to-state union-closed conjecture was true or false even after years. However, last winter saw a surge of interest in the conjec…
List packing number of bounded degree graphs
Stijn Cambie, Wouter Cames van Batenburg, Ewan Davies +1
We investigate the list packing number of a graph, the least such that there are always disjoint proper list-colourings whenever we have lists all of size associated to…
Packing colourings in complete bipartite graphs and the inverse problem for correspondence packing
Stijn Cambie, Rimma Hämäläinen
Applications of graph colouring often involve taking restrictions into account, and it is desirable to have multiple (disjoint) solutions. In the optimal case, where there is a par…
The maximum Wiener index of a uniform hypergraph
Stijn Cambie, Ervin Győri, Nika Salia +2
The Wiener index of a (hyper)graph is calculated by summing up the distances between all pairs of vertices. We determine the maximum possible Wiener index of a connected -vertex…
Many Hamiltonian subsets in large graphs with given density
Stijn Cambie, Jun Gao, Hong Liu
A set of vertices in a graph is a Hamiltonian subset if it induces a subgraph containing a Hamiltonian cycle. Kim, Liu, Sharifzadeh and Staden proved that among all graphs with min…