User profiles for Annika Heckel
Annika HeckelUppsala University Verified email at math.uu.se Cited by 122 |
The difference between the chromatic and the cochromatic number of a random graph
A Heckel - arXiv preprint arXiv:2409.17614, 2024 - arxiv.org
The cochromatic number $\zeta(G)$ of a graph $G$ is the minimum number of colours needed
for a vertex colouring where every colour class is either an independent set or a clique. …
for a vertex colouring where every colour class is either an independent set or a clique. …
The chromatic number of dense random graphs
A Heckel - Random Structures & Algorithms, 2018 - Wiley Online Library
The chromatic number of a graph G is defined as the minimum number of colors required for
a vertex coloring where no two adjacent vertices are colored the same. The chromatic …
a vertex coloring where no two adjacent vertices are colored the same. The chromatic …
Random triangles in random graphs
A Heckel - Random Structures & Algorithms, 2021 - Wiley Online Library
In a recent paper, Oliver Riordan shows that for and p up to and slightly larger than the threshold
for a K r ‐factor, the hypergraph formed by the copies of K r in G(n, p) contains a copy of …
for a K r ‐factor, the hypergraph formed by the copies of K r in G(n, p) contains a copy of …
Colouring random graphs: Tame colourings
A Heckel, K Panagiotou - arXiv preprint arXiv:2306.07253, 2023 - arxiv.org
Given a graph G, a colouring is an assignment of colours to the vertices of G so that no two
adjacent vertices are coloured the same. If all colour classes have size at most t, then we call …
adjacent vertices are coloured the same. If all colour classes have size at most t, then we call …
How does the chromatic number of a random graph vary?
A Heckel, O Riordan - Journal of the London Mathematical …, 2023 - Wiley Online Library
The chromatic number χ ( G ) $\chi (G)$ of a graph G $G$ is a fundamental parameter, whose
study was originally motivated by applications ( χ ( G ) $\chi (G)$ is the minimum number of …
study was originally motivated by applications ( χ ( G ) $\chi (G)$ is the minimum number of …
Non-concentration of the chromatic number of a random graph
A Heckel - Journal of the American Mathematical Society, 2021 - ams.org
… Annika Heckel … E-mail: heckel@maths.ox.ac.uk. This research was funded by ERC
Grant 676632. 1As usual, we say that a sequence (En)n∈N of events holds with high …
Grant 676632. 1As usual, we say that a sequence (En)n∈N of events holds with high …
Colourings of random graphs
A Heckel - 2016 - ora.ox.ac.uk
We study graph parameters arising from different types of colourings of random graphs,
defined broadly as an assignment of colours to either the vertices or the edges of a graph. The …
defined broadly as an assignment of colours to either the vertices or the edges of a graph. The …
The hitting time of clique factors
In [Trans. Am. Math. Soc. 375 (2022), no. 1, 627–668], Kahn gave the strongest possible,
affirmative, answer to Shamir's problem, which had been open since the late 1970s: Let r ⩾ 3 $…
affirmative, answer to Shamir's problem, which had been open since the late 1970s: Let r ⩾ 3 $…
Sharp Thresholds for Factors in Random Graphs
… , were obtained only recently by Riordan and Heckel, but only for complete graphs $F=K_r$ …
We extend the couplings by Riordan and Heckel to any strictly 1-balanced $F$ and thereby …
We extend the couplings by Riordan and Heckel to any strictly 1-balanced $F$ and thereby …
The hitting time of rainbow connection number two
A Heckel, O Riordan - arXiv preprint arXiv:1209.2981, 2012 - arxiv.org
In a graph $G$ with a given edge colouring, a rainbow path is a path all of whose edges
have distinct colours. The minimum number of colours required to colour the edges of $G$ so …
have distinct colours. The minimum number of colours required to colour the edges of $G$ so …