A decomposition of a graph ܩ is a collection of edge-disjoint subgraphs ܪଵ, ܪଶǡǥ ǡܪ௥ of ܩ
such that every edge of ܩ belongs to exactly one ܪ௜. In 2020, Hamiltonian decomposition of …

We show that if $ C_1 $ and $ C_2 $ are directed cycles (of length at least two), then the
Cartesian product $ C_1\Box C_2 $ has two arc-disjoint hamiltonian paths.(This answers a …

The Hamilton decomposition of graph G is a partition of the edge set into a Hamilton cycle
and 1-factor if the vertex degree is odd or a partition into a Hamilton cycle if the degree of the …

This dissertation aims to make a step towards a deeper understanding of ends of infinite
graphs. This first chapter serves the purpose of giving a concise introduction and an …

A well-known result of Benjamini, Lyons, Peres, and Schramm states that if G is a finitely
generated Cayley graph of a group Γ, then Γ is amenable if and only if G admits a Γ-invariant …

We prove that for all countable tournaments $ D $ the recently discovered compactification
$| D| $ by their ends and limit edges contains a topological Hamilton path: a topological arc …

A well‐known conjecture of Alspach says that every 2 k 2k‐regular Cayley graph of a finite
abelian group can be decomposed into Hamiltonian cycles. We consider an analogous …

A classical notion in graph theory is that of the block-cut vertex tree of a graph. It tells us that
if we consider the maximal 2-connected components of a connected graph G then they are …

We say that two graphs G and H are (vertex-) hypomorphic if there exists a bijection ϕ
between the vertices of G and H such that the induced subgraphs G− v and H− ϕ (v) are …