Graphs That Admit 3-to-1 or 2-to-1 Maps onto the Circle

نویسندگان

  • Anthony J. W. Hilton
  • Jiping Liu
  • Cheng Zhao
چکیده

We give a complete and explicit characterization of the connected graphs which admit a continuous 3-to-1 map onto the circle, and of the connected graphs which admit a continuous 2-to-l map onto the circle. This generalizes earlier work of Heath and Hilton who considered the mappings of trees onto the circle.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Extremal Problems for Star Mappings

The results obtained in §§1-2 are applied in §3 to show that the maximum possible value of dt{B log/'(z) + C log [/(z)/z]} at a point Zo of the unit circle, for the class of functions f(z) =z+ • • • which map |z| <1 conformally onto star-shaped regions, is attained for a function w=f(z) which maps the unit circle onto the w-plane with one or two radial slits. In §§4-5, we decide between these t...

متن کامل

Great Circle Challenge and Odd Graphs

Edge (5, 3)-colorings of a (5, 3)-regular bipartite graph relating 5cycles and vertices of the Petersen graph lead to solutions of the Great Circle Challenge. This takes, for odd n = 2k + 1 > 1, to a canonical 1-1 correspondence from the family of n-cycles of the complete graph Kn onto the family Ck of n-cycles of the odd graph Ok+1 and onto the family of their pullback 2n-cycles in the middle-...

متن کامل

Odd Graphs and the Great Circle Challenge

Edge (5, 3)-bicolorings of a (5, 3)-regular bipartite graph relating 5cycles and vertices of the Petersen graph lead to solutions of the Great Circle Challenge puzzle. This takes for odd n = 2k + 1 > 1 to a oneto-one correspondence from the family Cn of n-cycles of Kn onto the family Ok of n-cycles of the odd graph Ok+1. It also takes for odd l with 3 ≤ l ≤ ⌊n/2⌋ to a graph having Ok as vertex ...

متن کامل

Primal-dual Circle packing of Planar Maps

This work is based on Mohar [1]’s recent algorithm for circle packing for the Euclean case. We implement his polynomial time algorithm for constructing primal-dual circle packings of almost 3-connected planar maps. We have improved Mohar’s algorithm and have been able to get near an order of magnitude speed up for large graphs. We describe our implementation in C/C++ style pseudo-code.

متن کامل

Edge pair sum labeling of some cycle related graphs

Let G be a (p,q) graph. An injective map f : E(G) → {±1,±2,...,±q} is said to be an edge pair sum labeling if the induced vertex function f*: V (G) → Z - {0} defined by f*(v) = ΣP∈Ev f (e) is one-one where Ev denotes the set of edges in G that are incident with a vertex v and f*(V (G)) is either of the form {±k1,±k2,...,±kp/2} or {±k1,±k2,...,±k(p-1)/2} U {±k(p+1)/2} according as p is even or o...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Discrete Applied Mathematics

دوره 65  شماره 

صفحات  -

تاریخ انتشار 1996