Long cycles in graphs with no subgraphs of minimal degree 3
Discrete Mathematics
Induced subgraphs of the power of a cycle
SIAM Journal on Discrete Mathematics
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Approximation algorithms for NP-complete problems on planar graphs
Journal of the ACM (JACM)
Efficient Generation of Plane Triangulations without Repetitions
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STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
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FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
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Approximating Directed Weighted-Degree Constrained Networks
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
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APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
Degree-Constrained Subgraph Problems: Hardness and Approximation Results
Approximation and Online Algorithms
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Theoretical Computer Science
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IWPEC'08 Proceedings of the 3rd international conference on Parameterized and exact computation
On approximating the d-girth of a graph
SOFSEM'11 Proceedings of the 37th international conference on Current trends in theory and practice of computer science
Parameterized Complexity
On approximating the d-girth of a graph
SOFSEM'11 Proceedings of the 37th international conference on Current trends in theory and practice of computer science
On approximating the d-girth of a graph
Discrete Applied Mathematics
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For a finite, simple, undirected graph G and an integer d ≥ 1, a mindeg-d subgraph is a subgraph of G of minimum degree at least d. The d-girth of G, denoted gd(G), is the minimum size of a mindeg-d subgraph of G. It is a natural generalization of the usual girth, which coincides with the 2-girth. The notion of d-girth was proposed by Erdös et al. [13, 14] and Bollob10:03 AM 2/4/2011aacute;s and Brightwell [7] over 20 years ago, and studied from a purely combinatorial point of view. Since then, no new insights have appeared in the literature. Recently, first algorithmic studies of the problem have been carried out [2,4]. The current article further explores the complexity of finding a small mindeg-d subgraph of a given graph (that is, approximating its d-girth), by providing new hardness results and the first approximation algorithms in general graphs, as well as analyzing the case where G is planar.