Cicely Henderson

collaborators

5 papers

math.CO2026

Beyond Nash-Williams: Counterexamples to Clique Decomposition Thresholds for All Cliques Larger than Triangles

Michelle Delcourt, Cicely Henderson, Thomas Lesgourgues +1

A central open question in extremal design theory is Nash-Williams' Conjecture from 1970 that every $K_{3}$ -divisible graph on $n$ vertices (for $n$ large enough) with minimum degree…

math.CO2025

On the Hypergraph Nash-Williams' Conjecture

Cicely Henderson, Luke Postle

In 2014, Keevash proved the existence of $(n, q, r)$ -Steiner systems (equivalently $K_{q}^{r}$ -decompositions of $K_{n}^{r}$ ) for all large enough $n$ satisfying the necessary divisibility c…

math.CO2025

Maximum $k$ -colourable induced subgraphs in $(P_{5} + r K_{1})$ -free graphs

Cicely Henderson, Evelyne Smith-Roberge, Sophie Spirkl +1

We show that for any nonnegative integer $r$ , the Weighted Maximum List- $k$ -Colourable Induced Subgraph problem can be solved in polynomial time for input graphs that do not contai…

math.CO2025

Hamilton cycles in regular graphs perturbed by a random 2-factor

Cicely, Henderson, Sean Longbrake +2

In this paper, we prove that for each $d \geq 2$ , the union of a $d$ -regular graph with a uniformly random $2$ -factor on the same vertex set is Hamiltonian with high probability. T…

math.CO2025

ErdÅs meets Nash-Williams

Michelle Delcourt, Cicely, Henderson +2

In 1847, Kirkman proved that there exists a Steiner triple system on $n$ vertices (equivalently a triangle decomposition of the edges of $K_{n}$ ) whenever $n$ satisfies the necessary…

Beyond Nash-Williams: Counterexamples to Clique Decomposition Thresholds for All Cliques Larger than Triangles

On the Hypergraph Nash-Williams' Conjecture

Maximum k-colourable induced subgraphs in (P5​+rK1​)-free graphs

Hamilton cycles in regular graphs perturbed by a random 2-factor

ErdÅs meets Nash-Williams

Maximum $k$ -colourable induced subgraphs in $(P_{5} + r K_{1})$ -free graphs

ErdÅs meets Nash-Williams