New almost-planar crossing-critical graph families
نویسنده
چکیده
We show that, for all choices of integers k > 2 and m, there are simple 3-connected k-crossing-critical graphs containing more than m vertices of each even degree ≤ 2k − 2. This construction answers one half of a question raised by Bokal, while the other half asking analogously about vertices of odd degrees at least 5 in crossing-critical graphs remains open. Furthermore, our constructed graphs have several other interesting properties; for instance, they are almost planar and their average degree can attain any rational value in the interval
منابع مشابه
New Infinite Families of Almost-Planar Crossing-Critical Graphs
We show that, for all choices of integers k > 2 and m, there are simple 3connected k-crossing-critical graphs containing more than m vertices of each even degree ≤ 2k − 2. This construction answers one half of a question raised by Bokal, while the other half asking analogously about vertices of odd degrees at least 7 in crossing-critical graphs remains open. Furthermore, our newly constructed g...
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تاریخ انتشار 2007