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Abstract: For any given graph and an integer k, the number of connected components with k vertices in the graph is investigated. For the vertex set of size n and the maximum degree 1, the number is bounded above by (e1) k (101)k . The factor 1 k is essential, since we give the lower bound n 0 1 2 1 k01 for k ! 2n 1 . We also show that all connected components with k vertices are enumerable in O i n + m+ (e1) k 101 k 2 log k j time with O(n +m) space, where m is the number of edges.... (Update)
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BibTeX entry: (Update)
@misc{ uehara-number,
author = "Ryuhei Uehara",
title = "The Number of Connected Components in Graphs and Its Applications",
url = "citeseer.ist.psu.edu/199884.html" }
Citations (may not include all citations):1749 An Introduction to Probability Theory and Its Applications (context) - Feller - 1968
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222 Fixed-Parameter Tractability and Completeness I: Basic Resul.. - Downey, Fellows - 1995
222 Fixed-Parameter Tractability and Completeness II: On Comlete.. - Downey, Fellows - 1995
189 Parameterized Complexity - Downey, Fellows - 1999
132 Randomized Algorithms (context) - Motwani, Raghavan - 1995
51 The Minimum Latency Problem - Blum, Chalasani et al. - 1994
44 The Graph Isomorphism Problem: Its Structural Complexity (context) - Kobler, Schoning et al. - 1993
36 Spanning Trees Short or Small - Ravi, Sundaram et al. - 1994
22 Discrete Applied Mathematics (context) - Avis, Fukuda et al. - 1996
18 Color-Coding - Alon, Yuster et al. - 1995
16 Moderately Exponential Bound for Graph Isomorphism (context) - Babai - 1981
4 An Optimal Algorithm for Scanning All Spanning Trees of Undi.. - Shioura, Tamura et al. - 1997
3 Graph Isomorphism Problem (context) - Zemlyachenko, Korneenko et al. - 1985
1 Personal communication (context) - Uno - 1999
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