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
Discrete Mathematics
On the complexity of approximating the independent set problem
Information and Computation
Approximation algorithms for NP-complete problems on planar graphs
Journal of the ACM (JACM)
Efficient Generation of Plane Triangulations without Repetitions
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Approximating minimum-size k-connected spanning subgraphs via matching
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Networks
Discrete Applied Mathematics
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
A Constant Factor Approximation for Minimum λ-Edge-Connected k-Subgraph with Metric Costs
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
Hardness and approximation of traffic grooming
Theoretical Computer Science
Dynamic programming for graphs on surfaces
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
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 of finding small degree-constrained subgraphs
Journal of Discrete Algorithms
On the approximability of some degree-constrained subgraph problems
Discrete Applied Mathematics
Parameterized Complexity
| Hi-index | 0.04 |
For a finite, simple, undirected graph G and an integer d=1, a mindeg-dsubgraph is a subgraph of G of minimum degree at least d. The d-girth of G, denoted by g"d(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 Erdos et al. (1988, 1990) [14,15] and Bollobas and Brightwell (1989) [8] over 25 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 by Amini et al. (2012a,b) [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.