Generating 5‐regular planar graphs

Ding, Guoli; Kanno, Jinko; Su, Jianning

doi:10.1002/jgt.20377

Cited by 1 publication

(2 citation statements)

References 12 publications

(17 reference statements)

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“…When looking at the slope of the histogram, we can see that more than 99.6% of the faces of the generated graphs have a size within the interval [3,10]. The slope has its peak at size 3 and decreases fast with growing face size.…”

Section: A Appendixmentioning

confidence: 96%

“…Because every planar graph contains a vertex with degree at most 5, no 6-regular subgraph can occur in a planar graph. Although 5-regular graphs exist [10] their random generation seems to be unlikely as none of our generated graphs contains a 5-core. In Figure 6 the coreness distribution of graphs generated by the (n)-and (n,m)-generators using the Fusy distribution are shown.…”

Section: Algorithmical Behaviormentioning

confidence: 99%

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An Experimental Study on Generating Planar Graphs

Meinert

Wagner

2011

Frontiers in Algorithmics and Algorithmic Aspects in Information and Management

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Abstract. We survey several planar graph generators that were selected according to availability, theoretical interest, easiness of implementation and efficiency. We experimentally study graph properties that allow for a basic classification of the generators. This analysis is extended by means of advanced algorithmical behavior on the generated graphs, in particular kernelization of fixed-parameter tractable problems. We will see the major influence of instance selection on algorithmic behavior. This selection has been disregarded in several publications, which deduce general results from non-representative data sets. Altogether, this study helps experimenters to carefully select sets of planar graphs that allow for a meaningful interpretation of their results.

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Section: A Appendixmentioning

confidence: 96%

Section: Algorithmical Behaviormentioning

confidence: 99%