On Counting Independent Sets in Sparse Graphs
نویسندگان
چکیده
We prove two results concerning approximate counting of independent sets in graphs with constant maximum degree ∆. The first implies that the Markov chain Monte Carlo technique is likely to fail if ∆ ≥ 6. The second shows that no fully polynomial randomized approximation scheme can exist for ∆ ≥ 25, unless RP = NP.
منابع مشابه
A family of metrics for biopolymers based on counting independent sets
We introduce a new family of metrics for graphs of fixed size, based on counting-independent sets. Our definition is simpler and easier to calculate than the edge ideal metric family defined by Llabrés and Rosselló without loosing any of its abstract properties. We contrast them on some examples with graphs that represent protein secondary and three-dimensional (3D) structures. We conclude that...
متن کاملCounting independent sets in graphs
In this short survey article, we present an elementary, yet quite powerful, method of enumerating independent sets in graphs. This method was first employed more than three decades ago by Kleitman and Winston and has subsequently been used numerous times by many researchers in various contexts. Our presentation of the method is illustrated with several applications of it to ‘real-life’ combinat...
متن کامل2 9 A pr 2 01 2 INDEPENDENT SETS IN HYPERGRAPHS
Many important theorems and conjectures in combinatorics, such as the theorem of Szemerédi on arithmetic progressions and the Erd˝ os-Stone Theorem in extremal graph theory, can be phrased as statements about families of independent sets in certain uniform hypergraphs. In recent years, an important trend in the area has been to extend such classical results to the so-called 'sparse random setti...
متن کاملIndependent Sets in Hypergraphs
Many important theorems and conjectures in combinatorics, such as the theorem of Szemerédi on arithmetic progressions and the Erdős-Stone Theorem in extremal graph theory, can be phrased as statements about families of independent sets in certain uniform hypergraphs. In recent years, an important trend in the area has been to extend such classical results to the so-called ‘sparse random setting...
متن کاملThe Complexity of Counting in Sparse, Regular, and Planar Graphs
We show that a number of graph-theoretic counting problems remain NP-hard, indeed #P-complete, in very restricted classes of graphs. In particular, it is shown that the problems of counting matchings, vertex covers, independent sets, and extremal variants of these all remain hard when restricted to planar bipartite graphs of bounded degree or regular graphs of constant degree. To achieve these ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1999