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pro vyhledávání: '"and independence ratio."'
We prove that every $n$-vertex planar graph $G$ with no triangle sharing an edge with a 4-cycle has independence ratio $n/\alpha(G) \leq 4 - \varepsilon$ for $\varepsilon = 1/30$. This result implies that the same bound holds for 4-cycle-free planar
Externí odkaz:
http://arxiv.org/abs/2305.02414
Autor:
Harangi, Viktor
Studying independent sets of maximum size is equivalent to considering the hard-core model with the fugacity parameter $\lambda$ tending to infinity. Finding the independence ratio of random $d$-regular graphs for some fixed degree $d$ has received m
Externí odkaz:
http://arxiv.org/abs/2204.01353
Autor:
Harangi, Viktor1 (AUTHOR) harangi@renyi.hu
Publikováno v:
Journal of Statistical Physics. Mar2023, Vol. 190 Issue 3, p1-24. 24p.
Let $i(r,g)$ denote the infimum of the ratio $\frac{\alpha(G)}{|V(G)|}$ over the $r$-regular graphs of girth at least $g$, where $\alpha(G)$ is the independence number of $G$, and let $i(r,\infty) := \lim\limits_{g \to \infty} i(r,g)$. Recently, seve
Externí odkaz:
http://arxiv.org/abs/1708.03996
Autor:
Harangi, Viktor, Virág, Bálint
Publikováno v:
The Annals of Probability, 2015 Sep 01. 43(5), 2810-2840.
Externí odkaz:
http://www.jstor.org/stable/24520383
Autor:
Cranston, Daniel W., Rabern, Landon
Publikováno v:
Electronic Journal of Combinatorics. Vol. 23(3), 2016, #P3.45
The 4 Color Theorem (4CT) implies that every $n$-vertex planar graph has an independent set of size at least $\frac{n}4$; this is best possible, as shown by the disjoint union of many copies of $K_4$. In 1968, Erd\H{o}s asked whether this bound on in
Externí odkaz:
http://arxiv.org/abs/1609.06010
A distance graph is an undirected graph on the integers where two integers are adjacent if their difference is in a prescribed distance set. The independence ratio of a distance graph $G$ is the maximum density of an independent set in $G$. Lih, Liu,
Externí odkaz:
http://arxiv.org/abs/1401.7183
Autor:
Harangi, Viktor, Virág, Bálint
Publikováno v:
Annals of Probability 2015, Vol. 43, No. 5, 2810-2840
A theorem of Hoffman gives an upper bound on the independence ratio of regular graphs in terms of the minimum $\lambda_{\min}$ of the spectrum of the adjacency matrix. To complement this result we use random eigenvectors to gain lower bounds in the v
Externí odkaz:
http://arxiv.org/abs/1308.5173
We show that there are polynomial-time algorithms to compute maximum independent sets in the categorical products of two cographs and two splitgraphs. The ultimate categorical independence ratio of a graph G is defined as lim_{k --> infty} \alpha(G^k
Externí odkaz:
http://arxiv.org/abs/1306.1656
Autor:
Tóth, Ágnes
Brown, Nowakowski and Rall defined the ultimate categorical independence ratio of a graph G as A(G)=\lim_{k\to \infty} i(G^{\times k}), where i(G)=\frac{\alpha (G)}{|V(G)|} denotes the independence ratio of a graph G, and G^{\times k} is the k-th cat
Externí odkaz:
http://arxiv.org/abs/1112.6172