Thickness of graphs with degree constrained vertices

Bose, N.K.; Prabhu, K.

doi:10.1109/tcs.1977.1084323

Cited by 13 publications

(2 citation statements)

References 6 publications

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“…Due to the application in the design of integrated circuits, the degree-4 thickness y 4 G of a graph G has been de®ned as the minimal number of planar subgraphs with maximal degree four, whose union is G. Using an explicit construction, Bose and Prabhu [14] computed the degree-4 thickness of complete graphs in almost all cases.…”

Section: Modi®cations Of the Ground-conceptmentioning

confidence: 99%

The Thickness of Graphs: A Survey

Mutzel

Odenthal

Scharbrodt³

1998

Graphs Comb

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We give a state-of-the-art survey of the thickness of a graph from both a theoretical and a practical point of view. After summarizing the relevant results concerning this topological invariant of a graph, we deal with practical computation of the thickness. We present some modi®cations of a basic heuristic and investigate their usefulness for evaluating the thickness and determining a decomposition of a graph in planar subgraphs.

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Section: Modi®cations Of the Ground-conceptmentioning

confidence: 99%

The Thickness of Graphs: A Survey

Mutzel

Odenthal

Scharbrodt³

1998

Graphs Comb

View full text Add to dashboard Cite

show abstract

“…Even for the complete bipartite graph there are only partial results [7,13]. Some generalizations of the thickness for complete graphs have been studied, for instance, the outerthickness θ o , defined similarly but with outerplanar instead of planar [12], the S-thickness θ S , considering the thickness on a surface S instead of the plane [4], and the k-degree-thickness θ k taking a restriction on the planar subgraphs: each planar subgraph has maximum degree at most k [9].…”

Section: Introductionmentioning

confidence: 99%