TY - GEN

T1 - On approximating the d-girth of a graph

AU - Peleg, David

AU - Sau, Ignasi

AU - Shalom, Mordechai

PY - 2011

Y1 - 2011

N2 - 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 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. [13, 14] and Bollobás 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.

AB - 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 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. [13, 14] and Bollobás 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.

KW - approximation algorithm

KW - generalized girth

KW - hardness of approximation

KW - minimum degree

KW - planar graph

KW - randomized algorithm

UR - http://www.scopus.com/inward/record.url?scp=78751675706&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-18381-2_39

DO - 10.1007/978-3-642-18381-2_39

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AN - SCOPUS:78751675706

SN - 9783642183805

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 467

EP - 481

BT - SOFSEM 2011

T2 - 37th International Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2011

Y2 - 22 January 2011 through 28 January 2011

ER -