Graph colouring remains a central topic in graph theory, providing the mathematical framework for assigning colours to the elements of a graph under specific constraints. In particular, the ...

The term "minimal nonplanar subgraph" of a graph G refers to a nonplanar subgraph N of G having the property that each proper subgraph of N is planar. A well-known result of graph theory is that there ...

We prove that any distributional limit of finite planar graphs in which the degree of the root has an exponential tail is almost surely recurrent. As a corollary, we obtain that the uniform infinite ...

And it’s even harder to tell whether a complicated planar graph stays planar when you start adding edges as you might when planning a new stretch of highway. Computer scientists have been searching ...

Let us say that a graph is k- apex if it contains a set of at most k vertices whose removal yields a planar graph. We define the apex number of a graph G as the minimum k for which G is k-apex.