On the complexity of H-coloring
Journal of Combinatorial Theory Series B
Genus g graphs have pagenumber O g
Journal of Algorithms
Algorithms to count paths and cycles
Information Processing Letters
Journal of the ACM (JACM)
The complexity of counting graph homomorphisms
Proceedings of the ninth international conference on on Random structures and algorithms
Counting H-colorings of partial k-trees
Theoretical Computer Science
Coping with the NP-Hardness of the Graph Bandwidth Problem
SWAT '00 Proceedings of the 7th Scandinavian Workshop on Algorithm Theory
Moderately Exponential Bound for Graph Isomorphism
FCT '81 Proceedings of the 1981 International FCT-Conference on Fundamentals of Computation Theory
Splitters and near-optimal derandomization
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
A generating function approach to the Traveling Salesman Problem
ACM '77 Proceedings of the 1977 annual conference
Improved approximation algorithms for minimum-weight vertex separators
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
The complexity of counting homomorphisms seen from the other side
Theoretical Computer Science
Proper minor-closed families are small
Journal of Combinatorial Theory Series B
Inclusion--Exclusion Algorithms for Counting Set Partitions
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
An O*(2^n ) Algorithm for Graph Coloring and Other Partitioning Problems via Inclusion--Exclusion
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
The complexity of homomorphism and constraint satisfaction problems seen from the other side
Journal of the ACM (JACM)
Fourier meets möbius: fast subset convolution
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Computational complexity and the classification of finite simple groups
SFCS '83 Proceedings of the 24th Annual Symposium on Foundations of Computer Science
Exact Algorithms for Exact Satisfiability and Number of Perfect Matchings
Algorithmica - Parameterized and Exact Algorithms
Graph-Theoretic Concepts in Computer Science
Counting stars and other small subgraphs in sublinear time
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Capacitated domination faster than O(2n)
Information Processing Letters
Counting perfect matchings as fast as Ryser
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Capacitated domination faster than O(2n)
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
Faster algorithms for finding and counting subgraphs
Journal of Computer and System Sciences
Irredundant set faster than O(2n)
CIAC'10 Proceedings of the 7th international conference on Algorithms and Complexity
Learning from graph data by putting graphs on the lattice
Expert Systems with Applications: An International Journal
An exponential time 2-approximation algorithm for bandwidth
Theoretical Computer Science
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Counting homomorphisms between graphs has applications in variety of areas, including extremal graph theory, properties of graph products, partition functions in statistical physics and property testing of large graphs. In this work we show a new application of counting graph homomorphisms to the areas of exact and parameterized algorithms. We introduce a generic approach for counting subgraphs in a graph. The main idea is to relate counting subgraphs to counting graph homomorphisms. This approach provides new algorithms and unifies several well known results in algorithms and combinatorics including the recent algorithm of Björklund, Husfeldt and Koivisto for computing the chromatic polynomial, the classical algorithm of Kohn, Gottlieb, Kohn, and Karp for counting Hamiltonian cycles, Ryser's formula for counting perfect matchings of a bipartite graph, and color coding based algorithms of Alon, Yuster, and Zwick.