Jared León

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20242026

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5 papers · 1 filter

math.CO2025

Colour-biased Hamilton cycles in dense graphs and random graphs

Natalie Behague, Debsoumya Chakraborti, Jared LeÃ³n

A classical result of Dirac says that every $n$ -vertex graph with minimum degree at least $\frac{n}{2}$ contains a Hamilton cycle. A `discrepancy' version of Dirac's theorem was sh…

math.CO2025

The TurÃ¡n density of the tight 5-cycle minus one edge

Levente BodnÃ¡r, Jared LeÃ³n, Xizhi Liu +1

Let the tight $ℓ$ -cycle minus one edge $C_{ℓ}^{3 -}$ be the $3$ -graph on ${1, \dots, ℓ}$ consisting of $ℓ - 1$ consecutive triples in the cyclic order. We show that, for eve…

math.CO2025

The TurÃ¡n density of short tight cycles

Levente BodnÃ¡r, Jared LeÃ³n, Xizhi Liu +1

The $3$ -uniform tight $ℓ$ -cycle $C_{ℓ}^{3}$ is the $3$ -graph on ${1, \dots, ℓ}$ consisting of all $ℓ$ consecutive triples in the cyclic order. Let $C$ be either…

math.CO2025

Multi-cyclic graphs in the random graph process with restricted budget

Daniel IÄ¾koviÄ, Jared LeÃ³n, Xichao Shu

We study a controlled random graph process introduced by Frieze, Krivelevich, and Michaeli. In this model, the edges of a complete graph are randomly ordered and revealed sequentia…

math.CO2025

A Recolouring Version of a Conjecture of Reed

Reed conjectured that the chromatic number of any graph is closer to its clique number than to its maximum degree plus one. We consider a recolouring version of this conjecture, wi…