Zobrazeno 1 - 10
of 71
pro vyhledávání: '"Draganić, Nemanja"'
A connected dominating set (CDS) in a graph is a dominating set of vertices that induces a connected subgraph. Having many disjoint CDSs in a graph can be considered as a measure of its connectivity, and has various graph-theoretic and algorithmic im
Externí odkaz:
http://arxiv.org/abs/2410.16072
Autor:
Draganić, Nemanja, Montgomery, Richard, Correia, David Munhá, Pokrovskiy, Alexey, Sudakov, Benny
An $n$-vertex graph $G$ is a $C$-expander if $|N(X)|\geq C|X|$ for every $X\subseteq V(G)$ with $|X|< n/2C$ and there is an edge between every two disjoint sets of at least $n/2C$ vertices. We show that there is some constant $C>0$ for which every $C
Externí odkaz:
http://arxiv.org/abs/2402.06603
Autor:
Draganić, Nemanja, Keevash, Peter
We prove that any bounded degree regular graph with sufficiently strong spectral expansion contains an induced path of linear length. This is the first such result for expanders, strengthening an analogous result in the random setting by Dragani\'c,
Externí odkaz:
http://arxiv.org/abs/2402.02256
Autor:
Draganić, Nemanja, Nenadov, Rajko
We consider the problem of finding edge-disjoint paths between given pairs of vertices in a sufficiently strong $d$-regular expander graph $G$ with $n$ vertices. In particular, we describe a deterministic, polynomial time algorithm which maintains an
Externí odkaz:
http://arxiv.org/abs/2310.13082
In his seminal 1976 paper, P\'osa showed that for all $p\geq C\log n/n$, the binomial random graph $G(n,p)$ is with high probability Hamiltonian. This leads to the following natural questions, which have been extensively studied: How well is it typic
Externí odkaz:
http://arxiv.org/abs/2310.11580
Size-Ramsey numbers are a central notion in combinatorics and have been widely studied since their introduction by Erd\H{o}s, Faudree, Rousseau and Schelp in 1978. Research has mainly focused on the size-Ramsey numbers of $n$-vertex graphs with const
Externí odkaz:
http://arxiv.org/abs/2307.12028
How many edges in an $n$-vertex graph will force the existence of a cycle with as many chords as it has vertices? Almost 30 years ago, Chen, Erd\H{o}s and Staton considered this question and showed that any $n$-vertex graph with $2n^{3/2}$ edges cont
Externí odkaz:
http://arxiv.org/abs/2306.09157
The bipartite independence number of a graph $G$, denoted as $\tilde\alpha(G)$, is the minimal number $k$ such that there exist positive integers $a$ and $b$ with $a+b=k+1$ with the property that for any two sets $A,B\subseteq V(G)$ with $|A|=a$ and
Externí odkaz:
http://arxiv.org/abs/2302.12752
An $n$-vertex graph is Hamiltonian if it contains a cycle that covers all of its vertices and it is pancyclic if it contains cycles of all lengths from $3$ up to $n$. A celebrated meta-conjecture of Bondy states that every non-trivial condition imply
Externí odkaz:
http://arxiv.org/abs/2301.10190
The induced size-Ramsey number $\hat{r}_\text{ind}^k(H)$ of a graph $H$ is the smallest number of edges a (host) graph $G$ can have such that for any $k$-coloring of its edges, there exists a monochromatic copy of $H$ which is an induced subgraph of
Externí odkaz:
http://arxiv.org/abs/2301.10160