کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8900603 | 1631718 | 2018 | 15 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Regular non-hamiltonian polyhedral graphs
ترجمه فارسی عنوان
نمودار منظم غیر هامیلتونی
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات کاربردی
چکیده انگلیسی
Invoking Steinitz' Theorem, in the following a polyhedron shall be a 3-connected planar graph. From around 1880 till 1946 Tait's conjecture that cubic polyhedra are hamiltonian was thought to hold-its truth would have implied the Four Colour Theorem. However, Tutte gave a counterexample. We briefly survey the ensuing hunt for the smallest non-hamiltonian cubic polyhedron, the Lederberg-Bosák-Barnette graph, and prove that there exists a non-hamiltonian essentially 4-connected cubic polyhedron of order n if and only if nâ¯â¥â¯42. This extends work of Aldred, Bau, Holton, and McKay. We then present our main results which revolve around the quartic case: combining a novel theoretical approach for determining non-hamiltonicity in (not necessarily planar) graphs of connectivity 3 with computational methods, we dramatically improve two bounds due to Zaks. In particular, we show that the smallest non-hamiltonian quartic polyhedron has at least 35 and at most 39 vertices, thereby almost reaching a quartic analogue of a famous result of Holton and McKay. As an application of our results, we obtain that the shortness coefficient of the family of all quartic polyhedra does not exceed 5/6. The paper ends with a discussion of the quintic case in which we tighten a result of Owens.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied Mathematics and Computation - Volume 338, 1 December 2018, Pages 192-206
Journal: Applied Mathematics and Computation - Volume 338, 1 December 2018, Pages 192-206
نویسندگان
Nico Van Cleemput, Carol T. Zamfirescu,