کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4656722 1632974 2016 30 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Three-edge-colouring doublecross cubic graphs
ترجمه فارسی عنوان
گرافهای مکعبی دوبرابر سه لبه رنگی
کلمات کلیدی
لبه رنگ آمیزی، پترسن کوچک، قضیه چهار رنگ
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات گسسته و ترکیبات
چکیده انگلیسی

A graph is apex if there is a vertex whose deletion makes the graph planar, and doublecross if it can be drawn in the plane with only two crossings, both incident with the infinite region in the natural sense. In 1966, Tutte [9] conjectured that every two-edge-connected cubic graph with no Petersen graph minor is three-edge-colourable. With Neil Robertson, two of us showed that this is true in general if it is true for apex graphs and doublecross graphs [6] and [7]. In another paper [8], two of us solved the apex case, but the doublecross case remained open. Here we solve the doublecross case; that is, we prove that every two-edge-connected doublecross cubic graph is three-edge-colourable. The proof method is a variant on the proof of the four-colour theorem given in [5].

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Combinatorial Theory, Series B - Volume 119, July 2016, Pages 66–95
نویسندگان
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