We give a simple combinatorial description of an (n-2k+2)-chromatic edge-critical subgraph of the Schrijver graph SG(n,k), itself an induced vertex-critical subgraph of the Kneser graph KG(n,k). This extends the main result of Kaiser and Stehlík (2020) to all values of k, and sharpens&#...

A leaf matching operation on a graph consists of removing a vertex of degree 1 together with its neighbour from the graph. Let G be a d‐regular cyclically (d k − 1+2 )‐ edge‐connected graph of even order, where k ≥ 0 and d ≥ 3. We prove that for a...

We extend Szego--Weinberger type inequalities in various directions. We consider domains with holes with different type of symmetries as well as higher eigenvalues.

The class E(k) of hypergraphs with a k-exclusive sum labelling is hereditary, but non-trivial to characterise even for k=1. Our main result is a complete description of the minimal forbidden induced subhypergraphs of E(1) that are 3-uniform with maximum vertex degree 2. We also...

A fullerene graph is a 3-connected cubic planar graph with pentagonal and hexagonal faces. The leapfrog transformation of a planar graph produces the trucation of the dual of the given graph. A fullerene graph is leapfrog if it can be obtained from another fullerene graph ...