N. Dragani'c

activity

20242026

collaborators

8 papers

math.CO2026

The LovÃ¡sz conjecture holds for moderately dense Cayley graphs

Benjamin Bedert, Nemanja DraganiÄ, Alp MÃ¼yesser +1

We show that there is an absolute constant $c > 0$ such that every large connected $n$ -vertex Cayley graph with degree $d \geq n^{1 - c}$ has a Hamilton cycle. This makes progress towar…

math.CO2026

Cycles with almost linearly many chords

Nemanja DraganiÄ, AntÃ³nio GirÃ£o

We prove that constant minimum degree already forces cycles with almost linearly many chords. Specifically, every graph $G$ with $I^´ (G) \geq C$ contains a cycle of length $ℓ \geq 4$ …

math.CO2025

On Independent Spanning Trees in Random and Pseudorandom Graphs

Nemanja DraganiÄ, Keith Frankston, Michael Krivelevich +2

In 1989, Zehavi and Itai conjectured that every $k$ -connected graph contains $k$ independent spanning trees rooted at any prescribed vertex $r$ . That is, for each vertex $v$ , the u…

math.CO2025

Hamilton cycles in pseudorandom graphs: resilience and approximate decompositions

Nemanja DraganiÄ, Jaehoon Kim, Hyunwoo Lee +3

Dirac's classical theorem asserts that, for $n \geq 3$ , any $n$ -vertex graph with minimum degree at least $n /2$ is Hamiltonian. Furthermore, if we additionally assume that such grap…

math.CO2025

New bounds for linear arboricity and related problems

Micha Christoph, Nemanja DraganiÄ, AntÃ³nio GirÃ£o +3

A linear forest is a collection of vertex-disjoint paths. The Linear Arboricity Conjecture states that every graph of maximum degree $I^$ can be decomposed into at most $\lceil(Î+…

math.CO2025

Cyclic subsets in regular Dirac graphs

Nemanja DraganiÄ, Peter Keevash, Alp MÃ¼yesser

In 1996, in his last paper, ErdÅs asked the following question that he formulated together with Faudree: is there a positive $c$ such that any $(n + 1)$ -regular graph $G$ on $2 n$ ve…