T. Molla

activity

20132026

most citedOn Odd Rainbow Cycles in Edge-Colored Graphs

11 citations · 29 across the 14 of their papers we have counts for

collaborators

20 papers

math.CO2026

Maximizing $K_{r} + I_{r}$ in graphs with fixed edge density

József Balogh, Andrzej Grzesik, Bernard Lidický +3

For every integer $r \geq 4$ , and $ρ \in [0, 1]$ , we asymptotically determine the maximum proportion of $r$ -element sets of vertices that induce either a clique or an independent set in…

math.CO2026

Cycle tilings and $H$ -factors in directed graphs

Theodore Molla, Andrew Treglown

We prove several results concerning cycle tilings and $H$ -factors in digraphs. We provide a minimum semi-degree condition for forcing a digraph to contain a given spanning collecti…

math.CO2024

Powers of Hamilton cycles in oriented and directed graphs

Louis DeBiasio, Jie Han, Allan Lo +3

The Pósa--Seymour conjecture determines the minimum degree threshold for forcing the $k$ th power of a Hamilton cycle in a graph. After numerous partial results, Komlós, Sárközy and…

math.CO2021★ 4 cited

Powers of Hamiltonian cycles in multipartite graphs

Louis DeBiasio, Ryan Martin, Theodore Molla

We prove that if $G$ is a $k$ -partite graph on $n$ vertices in which all of the parts have order at most $n / r$ and every vertex is adjacent to at least a $1 - 1/ r + o (1)$ proportion of…

math.CO2021★ 1 cited

Transversal $C_{k}$ -factors in subgraphs of the balanced blow-up of $C_{k}$

Beka Ergemlidze, Theodore Molla

For a subgraph $G$ of the blow-up of a graph $F$ , we let $δ^{*} (G)$ be the smallest minimum degree over all of the bipartite subgraphs of $G$ induced by pairs of parts that correspon…

math.CO2019

On Even Rainbow or Nontriangular Directed Cycles

Andrzej Czygrinow, Theodore Molla, Brendan Nagle +1

Let $G = (V, E)$ be an $n$ -vertex edge-colored graph. In 2013, H. Li proved that if every vertex $v \in V$ is incident to at least $(n + 1) /2$ distinctly colored edges, then $G$ admi…

math.CO2019★ 11 cited

On Odd Rainbow Cycles in Edge-Colored Graphs

Andrzej Czygrinow, Theodore Molla, Brendan Nagle +1

Let $G = (V, E)$ be an $n$ -vertex edge-colored graph. In 2013, H. Li proved that if every vertex $v \in V$ is incident to at least $(n + 1) /2$ distinctly colored edges, then $G$ admi…

math.CO2019

Transitive tournament tilings in oriented graphs with large minimum total degree

Louis DeBiasio, Allan Lo, Theodore Molla +1

Let $T_{k}$ be the transitive tournament on $k$ vertices. We show that every oriented graph on $n = 4 m$ vertices with minimum total degree $(11/12 + o (1)) n$ can be partitioned into…

math.CO2018

Cyclic triangle factors in regular tournaments

Lina Li, Theodore Molla

Both Cuckler and Yuster independently conjectured that when $n$ is an odd positive multiple of $3$ every regular tournament on $n$ vertices contains a collection of $n /3$ vertex-di…

math.CO2017

Long rainbow cycles and Hamiltonian cycles using many colors in properly edge-colored complete graphs

Jozsef Balogh, Theodore Molla

We prove two results regarding cycles in properly edge-colored graphs. First, we make a small improvement to the recent breakthrough work of Alon, Pokrovskiy and Sudakov who showed…

math.CO2016

Triangle-tilings in graphs without large independent sets

József Balogh, Andrew McDowell, Theodore Molla +1

We study the minimum degree necessary to guarantee the existence of perfect and almost-perfect triangle-tilings in an $n$ -vertex graph $G$ with sublinear independence number. In th…

math.CO2016

Tiling directed graphs with tournaments

Andrzej Czygrinow, Louis DeBiasio, Theodore Molla +1

The Hajnal--Szemerédi theorem states that for any integer $r \geq 1$ and any multiple $n$ of $r$ , if $G$ is a graph on $n$ vertices and $δ (G) \geq (1 - 1/ r) n$ , then $G$ can be partit…

math.CO2015

A refinement of theorems on vertex-disjoint chorded cycles

Theodore Molla, Michael Santana, Elyse Yeager

In 1963, Corrádi and Hajnal settled a conjecture of Erdős by proving that, for all $k \geq 1$ , any graph $G$ with $∣ G ∣ \geq 3 k$ and minimum degree at least $2 k$ contains $k$ vertex…

math.CO2015★ 4 cited

Increasing paths in edge-ordered graphs: the hypercube and random graphs

Jessica De Silva, Theodore Molla, Florian Pfender +2

An edge-ordering of a graph $G = (V, E)$ is a bijection $ϕ : E \to {1, 2, ..., ∣ E ∣}$ . Given an edge-ordering, a sequence of edges $P = e_{1}, e_{2}, ..., e_{k}$ is an increasing path if it is a path…

math.CO2014

Arbitrary Orientations of Hamilton Cycles in Digraphs

Louis DeBiasio, Daniela Kühn, Theodore Molla +2

Let $n$ be sufficiently large and suppose that $G$ is a digraph on $n$ vertices where every vertex has in- and outdegree at least $n /2$ . We show that $G$ contains every orientation…

math.CO2014★ 6 cited

Transitive Triangle Tilings in Oriented Graphs

József Balogh, Allan Lo, Theodore Molla

In this paper, we prove an analogue of Corrádi and Hajnal's classical theorem. There exists $n_{0}$ such that for every $n \in 3 Z$ when $n \geq n_{0}$ the following holds. If $…

math.CO2013

On directed versions of the Corrádi-Hajnal Corollary

Andrzej Czygrinow, H. A. Kierstead, Theodore Molla

For $k \in N$ , Corrádi and Hajnal proved that every graph $G$ on $3 k$ vertices with minimum degree $δ (G) \geq 2 k$ has a $C_{3}$ -factor, i.e., a partitioning of the vertex set…

math.CO2013★ 2 cited

Tight co-degree condition for the existence of loose Hamilton cycles in 3-graphs

Andrzej Czygrinow, Theodore Molla

In 2006, Kühn and Osthus showed that if a 3-graph H on n vertices has minimum co-degree at least (1/4 +o(1))n and n is even then H has a loose Hamilton cycle. In this paper, we pro…

math.CO2013

Semi-degree threshold for anti-directed Hamiltonian cycles

Louis DeBiasio, Theodore Molla

In 1960, Ghouila-Houri extended Dirac's theorem to directed graphs by proving that if D is a directed graph on n vertices with minimum out-degree and in-degree at least n/2 (i.e. m…

math.CO2013★ 1 cited

An extension of the Hajnal-Szemeredi theorem to directed graphs

Andrzej Czygrinow, Louis DeBiasio, H. A. Kierstead +1

Hajnal and Szemeredi proved that every graph G with |G|=ks and minimum degree at least k(s-1) contains k vertex disjoint s-cliques; moreover this degree bound is optimal. We extend…