Zobrazeno 1 - 10
of 501
pro vyhledávání: '"Haslegrave A."'
Autor:
Haslegrave, John, Keevash, Peter
We consider a general framework for multi-type interacting particle systems on graphs, where particles move one at a time by random walk steps, different types may have different speeds, and may interact, possibly randomly, when they meet. We study t
Externí odkaz:
http://arxiv.org/abs/2404.04149
Autor:
Haslegrave, John, Keevash, Peter
We consider an interacting particle system where equal-sized populations of two types of particles move by random walk steps on a graph, the two types may have different speeds, and meetings of opposite-type particles result in annihilation. The key
Externí odkaz:
http://arxiv.org/abs/2404.04128
We investigate how small the Randi\'c index of a graph can be in terms of its matching number, and prove several results. We give best-possible linear bounds for graphs of small excess and for subcubic graphs; in the former case the size of excess we
Externí odkaz:
http://arxiv.org/abs/2402.12884
Autor:
Haslegrave, John
O and Shi proved that the Randi\'c index of any graph $G$ with minimum degree at least $\delta$ and maximum degree at most $\Delta$ is at least $\frac{\sqrt{\delta\Delta}}{\delta+\Delta}|G|$, with equality if and only if the graph is $(\delta,\Delta)
Externí odkaz:
http://arxiv.org/abs/2402.01346
The boundary rigidity problem is a classical question from Riemannian geometry: if $(M, g)$ is a Riemannian manifold with smooth boundary, is the geometry of $M$ determined up to isometry by the metric $d_g$ induced on the boundary $\partial M$? In t
Externí odkaz:
http://arxiv.org/abs/2309.04385
We extend the two-type preferential attachment model of Antunovi\'c, Mossel and R\'acz to networks with community structure. We show that different types of limiting behaviour can be found depending on the choice of community structure and type assig
Externí odkaz:
http://arxiv.org/abs/2212.13235
Autor:
Haslegrave, John
Publikováno v:
Discrete Applied Mathematics Volume 340 (2023), Pages 79-84
Foucaud, Krishna and Lekshmi recently introduced the concept of monitoring edge-geodetic sets in graphs, and a related graph invariant. These are sets of vertices such that the removal of any edge changes the distance between some pair of vertices in
Externí odkaz:
http://arxiv.org/abs/2210.08955
Publikováno v:
Discrete Mathematics Volume 347, Issue 4, April 2024, 113850
The chromatic edge stability index $\mathrm{es}_{\chi'}(G)$ of a graph $G$ is the minimum number of edges whose removal results in a graph with smaller chromatic index. We give best-possible upper bounds on $\mathrm{es}_{\chi'}(G)$ in terms of the nu
Externí odkaz:
http://arxiv.org/abs/2206.03953
Publikováno v:
European Journal of Combinatorics Volume 115, January 2024, 103781
How large must the chromatic number of a graph be, in terms of the graph's maximum degree, to ensure that the most efficient way to reduce the chromatic number by removing vertices is to remove an independent set? By a reduction to a powerful, known
Externí odkaz:
http://arxiv.org/abs/2203.13833
Publikováno v:
Forum of Mathematics, Sigma , Volume 11 , 2023 , e10
The Ramsey number $R(F,H)$ is the minimum number $N$ such that any $N$-vertex graph either contains a copy of $F$ or its complement contains $H$. Burr in 1981 proved a pleasingly general result that for any graph $H$, provided $n$ is sufficiently lar
Externí odkaz:
http://arxiv.org/abs/2112.03893