6 papers
End-faithful spanning trees in graphs without normal spanning trees
Carl Bürger, Jan Kurkofka
Schmidt characterised the class of rayless graphs by an ordinal rank function, which makes it possible to prove statements about rayless graphs by transfinite induction. Halin aske…
Duality theorems for stars and combs II: Dominating stars and dominated combs
Carl Bürger, Jan Kurkofka
In a series of four papers we determine structures whose existence is dual, in the sense of complementary, to the existence of stars or combs. Here, in the second paper of the seri…
Duality theorems for stars and combs III: Undominated combs
Carl Bürger, Jan Kurkofka
In a series of four papers we determine structures whose existence is dual, in the sense of complementary, to the existence of stars or combs. Here, in the third paper of the serie…
Duality theorems for stars and combs IV: Undominating stars
Carl Bürger, Jan Kurkofka
In a series of four papers we determine structures whose existence is dual, in the sense of complementary, to the existence of stars or combs. In the first paper of our series we d…
Partitioning edge-coloured infinite complete bipartite graphs into monochromatic paths
Carl Bürger, Max Pitz
In 1978, Richard Rado showed that every edge-coloured complete graph of countably infinite order can be partitioned into monochromatic paths of different colours. He asked whether…
Partitioning Edge-Coloured Complete Symmetric Digraphs into Monochromatic Complete Subgraphs
Carl Bürger, Louis DeBiasio, Hannah Guggiari +1
Let be the complete symmetric digraph on the positive integers. Answering a question of DeBiasio and McKenney, we construct a -colouring of the edges of $K_{\ma…