A note on bipartite subgraphs of triangle-free regular graphs
Journal of Graph Theory
On the power of unique 2-prover 1-round games
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Bipartite density of cubic graphs
Discrete Mathematics
On the Hardness of Approximating Max k-Cut and Its Dual
On the Hardness of Approximating Max k-Cut and Its Dual
Homomorphisms from sparse graphs with large girth
Journal of Combinatorial Theory Series B
Every 2-CSP allows nontrivial approximation
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
MAX k-CUT and approximating the chromatic number of random graphs
Random Structures & Algorithms
Approximating almost all instances of MAX-CUT within a ratio above the håstad threshold
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Optimal Inapproximability Results for MAX-CUT and Other 2-Variable CSPs?
SIAM Journal on Computing
Optimal algorithms and inapproximability results for every CSP?
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Planar Graphs of Odd-Girth at Least $9$ are Homomorphic to the Petersen Graph
SIAM Journal on Discrete Mathematics
Approximation algorithms for graph homomorphism problems
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
Ruling out polynomial-time approximation schemes for hard constraint satisfaction problems
CSR'07 Proceedings of the Second international conference on Computer Science: theory and applications
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A graph homomorphism is a vertex map which carries edges from a source graph to edges in a target graph. We study the approximability properties of the Weighted Maximum H -Colourable Subgraph problem (Max H -Col ). The instances of this problem are edge-weighted graphs G and the objective is to find a subgraph of G that has maximal total edge weight, under the condition that the subgraph has a homomorphism to H ; note that for H = K k this problem is equivalent to Max k -cut . To this end, we introduce a metric structure on the space of graphs which allows us to extend previously known approximability results to larger classes of graphs. Specifically, the approximation algorithms for Max cut by Goemans and Williamson and Max k -cut by Frieze and Jerrum can be used to yield non-trivial approximation results for Max H -Col . For a variety of graphs, we show near-optimality results under the Unique Games Conjecture. We also use our method for comparing the performance of Frieze & Jerrum's algorithm with Håstad's approximation algorithm for general Max 2-Csp . This comparison is, in most cases, favourable to Frieze & Jerrum.