Describing (d−2)-stars at d-vertices, d≤5, in normal plane maps
نویسندگان
چکیده
منابع مشابه
Describing 3-paths in normal plane maps
We prove that every normal plane map, as well as every 3polytope, has a path on three vertices whose degrees are bounded from above by one of the following triplets: $(3,3,\infty)$, $(3,4,11)$, $(3,7,6)$, $(3,10,4)$, $(3,15,3)$, $(4,4,9)$, $(6,4,8)$, $(7,4,7)$, and $(6,5,6)$. No parameter of this description can be improved, as shown by appropriate 3-polytopes. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 ...
متن کامل5-stars of Low Weight in Normal Plane Maps with Minimum Degree 5
It is known that there are normal plane maps M5 with minimum degree 5 such that the minimum degree-sum w(S5) of 5-stars at 5-vertices is arbitrarily large. In 1940, Lebesgue showed that if an M5 has no 4-stars of cyclic type (5, 6, 6, 5) centered at 5-vertices, then w(S5) ≤ 68. We improve this bound of 68 to 55 and give a construction of a (5, 6, 6, 5)-free M5 with w(S5) = 48.
متن کاملVertices of Plane Curves
PROOF. Apply Theorem J for the case w==r. We obtain for gr an expression which differs from the one just written only in the fact that the terms Brtr+ifr+i+Brtr+2fr+2+ • • • +Br,nfn are missing from its numerator. But the coefficients J3r,, = 0 when r<s. Hence the two expressions are equal. REMARK. The generalization of the method to orthonormalization with respect to a general norming or weigh...
متن کاملOn doubly light vertices in plane graphs
A vertex is said to be doubly light in a family of plane graphs if its degree and sizes of neighbouring faces are bounded above by a finite constant. We provide several results on the existence of doubly light vertices in various families of plane graph.
متن کاملOn the structural result on normal plane maps
We prove the structural result on normal plane maps, which applies to the vertex distance colouring of plane maps. The vertex distance-t chromatic number of a plane graph G with maximum degree ∆(G) ≤ D, D ≥ 12 is proved to be upper bounded by 6+ 2D+12 D−2 ((D−1)(t−1)−1). This improves a recent bound 6 + 3D+3 D−2 ((D − 1)t−1 − 1), D ≥ 8 by Jendrol’ and Skupień, and the upper bound for distance-2...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2013
ISSN: 0012-365X
DOI: 10.1016/j.disc.2013.04.026