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pro vyhledávání: '"05C80"'
This is the first of two complementary works in which we analyze the connected components of the degree-corrected stochastic block model (DCSBM). Our model is a random graph with an underlying community structure and degree in-homogeneity. It belongs
Externí odkaz:
http://arxiv.org/abs/2409.18894
Let $r \ge 3 $, let $n$ be divisible by $r$ and consider the random graph process on $n$ vertices. It was shown recently that in the random graph process, as soon as every vertex is covered by a copy of the complete graph $K_r$, a $K_r$-factor exists
Externí odkaz:
http://arxiv.org/abs/2409.17764
Autor:
Heckel, Annika
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. Let $\chi(G)$ denote the usual chromatic number. Around 1991 Erd\H{o}s
Externí odkaz:
http://arxiv.org/abs/2409.17614
We introduce a spatiotemporal self-exciting point process $(N_t(x))$, boundedly finite both over time $[0,\infty)$ and space $\mathscr X$, with excitation structure determined by a graphon $W$ on $\mathscr X^2$. This graphon Hawkes process generalize
Externí odkaz:
http://arxiv.org/abs/2409.16903
Given a directed graph, the Minimal Feedback Arc Set (FAS) problem asks for a minimal set of arcs in a directed graph, which, when removed, results in an acyclic graph. Equivalently, the FAS problem asks to find an ordering of the vertices that minim
Externí odkaz:
http://arxiv.org/abs/2409.16443
Autor:
Liu, Qingwei, Privault, Nicolas
This paper studies the limiting behavior of the count of subgraphs isomorphic to a graph $G$ with $m\geq 0$ fixed endpoints in the random-connection model, as the intensity $\lambda$ of the underlying Poisson point process tends to infinity. When con
Externí odkaz:
http://arxiv.org/abs/2409.16222
Autor:
Diskin, Sahar, Geisler, Anna
Let $d,n\in \mathbb{N}$ be such that $d=\omega(1)$, and $d\le n^{1-a}$ for some constant $a>0$. Consider a $d$-regular graph $G=(V, E)$ and the random graph process that starts with the empty graph $G(0)$ and at each step $G(i)$ is obtained from $G(i
Externí odkaz:
http://arxiv.org/abs/2409.14398
Autor:
Long, Eoin, Ploscaru, Laurentiu
Given an $n$-vertex graph $G$, let $\hom (G)$ denote the size of a largest homogeneous set in $G$ and let $f(G)$ denote the maximal number of distinct degrees appearing in an induced subgraph of $G$. The relationship between these parameters has been
Externí odkaz:
http://arxiv.org/abs/2409.14134
We consider a Gibbs distribution over all spanning trees of an undirected, edge weighted finite graph, where, up to normalization, the probability of each tree is given by the product of its edge weights. Defining the weighted degree of a node as the
Externí odkaz:
http://arxiv.org/abs/2409.13472
In this paper we show that the random degree constrained process (a time-evolving random graph model with degree constraints) has a local weak limit, provided that the underlying host graphs are high degree almost regular. We, moreover, identify the
Externí odkaz:
http://arxiv.org/abs/2409.11747