Large independent sets in regular graphs of large girth
نویسندگان
چکیده
منابع مشابه
Large independent sets in regular graphs of large girth
Let G be a d-regular graph with girth g, and let α be the independence number of G. We show that α(G) ≥ 12 ( 1− (d− 1)−2/(d−2) − (g) ) n where (g) → 0 as g → ∞, and we compute explicit bounds on (g) for small g. For large g this improves previous results for all d ≥ 7. The method is by analysis of a simple greedy algorithm which was motivated by the differential equation method used to bound in...
متن کاملIndependent sets and cuts in large-girth regular graphs
We present a local algorithm producing an independent set of expected size 0.44533n on large-girth 3-regular graphs and 0.40407n on large-girth 4-regular graphs. We also construct a cut (or bisection or bipartite subgraph) with 1.34105n edges on large-girth 3regular graphs. These decrease the gaps between the best known upper and lower bounds from 0.0178 to 0.01, from 0.0242 to 0.0123 and from ...
متن کاملLarge k-independent sets of regular graphs
We present a simple, yet efficient, heuristic for finding a large 2-independent set of regular graphs. We analyse the average-case performance of this heuristic, which is a randomised greedy algorithm, by analysing its performance on random regular graphs using differential equations. In this way, we prove lower bounds on the expected size of a largest 2-independent set of random regular graphs...
متن کاملLocally Dense Independent Sets in Regular Graphs of Large Girth - An Example of a New Approach
For an integer d ≥ 3 let α(d) be the supremum over all α with the property that for every > 0 there exists some g( ) such that every d-regular graph of order n and girth at least g( ) has an independent set of cardinality at least (α− )n. Extending an approach proposed by Lauer and Wormald (Large independent sets in regular graphs of large girth, J. Comb. Theory, Ser. B 97 (2007), 999-1009) and...
متن کاملInvariant Gaussian processes and independent sets on regular graphs of large girth
We prove that every 3-regular, n-vertex simple graph with sufficiently large girth contains an independent set of size at least 0.4361n. (The best known bound is 0.4352n.) In fact, computer simulation suggests that the bound our method provides is about 0.438n. Our method uses invariant Gaussian processes on the d-regular tree that satisfy the eigenvector equation at each vertex for a certain e...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 2007
ISSN: 0095-8956
DOI: 10.1016/j.jctb.2007.02.006