The arboricity Γ (G) of an undirected graph G=(V, E) is the minimal number k such that E can
be partitioned into k forests. Nash–Williams' formula states that k=⌈ γ (G)⌉, where γ (G) is …

In extremal combinatorics, it is common to focus on structures that are minimal with respect
to a certain property. In particular, critical and list-critical graphs occupy a prominent place in …

Brooks' Theorem from 1941 is a cornerstone in graph theory. Until then graph coloring
theory was centered around planar graphs and the four color problem. Brooks' Theorem was …

While planar graphs are flat from a topological viewpoint, we observe that they are not from
a geometric one. We prove that every planar graph can be embedded into a surface …

Let 𝑁 be a network (or linear graph) such that at each node not more than 𝑛 lines meet
(where 𝑛> 2), and no line has both ends at the same node. Suppose also that no connected …