The Maximum of the Maximum Rectilinear Crossing Numbers of $d$-Regular Graphs of Order $n$

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The Maximum of the Maximum Rectilinear Crossing Numbers of d-Regular Graphs of Order n

We extend known results regarding the maximum rectilinear crossing number of the cycle graph (Cn) and the complete graph (Kn) to the class of general d-regular graphs Rn,d. We present the generalized star drawings of the d-regular graphs Sn,d of order n where n + d ≡ 1 (mod 2) and prove that they maximize the maximum rectilinear crossing numbers. A star-like drawing of Sn,d for n ≡ d ≡ 0 (mod 2...

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Maximum Rectilinear Crossing Number

The problem of drawing a graph in the plane with a minimum number of edge crossings—called the crossing number of a graph—is a well-studied problem which dates back to the first half of the twentieth century, as mentioned in [11], and was formulated in full generality in [3]. It was shown that this problem is NP-Complete [4], and that it remains so even when restricted to cubic graphs [5]. Many...

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Approximating the Maximum Rectilinear Crossing Number

The problem of drawing a graph in the plane with a minimum number of edge crossings—called the crossing number of a graph—is a well-studied problem which dates back to the first half of the twentieth century, as mentioned in [11], and was formulated in full generality in [3]. It was shown that this problem is NP-Complete [4], and that it remains so even when restricted to cubic graphs [5]. Many...

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ژورنال

عنوان ژورنال: The Electronic Journal of Combinatorics

سال: 2009

ISSN: 1077-8926

DOI: 10.37236/143