Every Triangulated 3-Polytope of Minimum Degree 4 has a 4-Path of Weight at Most 27
نویسندگان
چکیده
By δ and wk denote the minimum degree and minimum degree-sum (weight) of a k-vertex path in a given graph, respectively. For every 3-polytope, w2 6 13 (Kotzig, 1955) and w3 6 21 (Ando, Iwasaki, Kaneko, 1993), where both bounds are sharp. For every 3-polytope with δ > 4, we have sharp bounds w2 6 11 (Lebesgue, 1940) and w3 6 17 (Borodin, 1997). Madaras (2000) proved that every triangulated 3-polytope with δ > 4 satisfies w4 6 31 and constructed such a 3-polytope with w4 = 27. We improve the Madaras bound w4 6 31 to the sharp bound w4 6 27.
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ورودعنوان ژورنال:
- Electr. J. Comb.
دوره 23 شماره
صفحات -
تاریخ انتشار 2016