𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Infinite families of biembedding numbers

✍ Scribed by I. Anderson


Publisher
John Wiley and Sons
Year
1979
Tongue
English
Weight
244 KB
Volume
3
Category
Article
ISSN
0364-9024

No coin nor oath required. For personal study only.

✦ Synopsis


Abstract

Let N(γ, γ′) denote the size of the smallest complete graph that cannot be edge‐partitioned into two parts embeddable in closed orientable sufaces of genera γ, γ′, respectively. Well‐known embedding theorems are used to obtain several infinite families of values of N(γ, γ′). Some related small values of N(γ, γ′) are also discussed.


📜 SIMILAR VOLUMES


Infinite families of crossing-critical g
✍ Drago Bokal 📂 Article 📅 2010 🏛 John Wiley and Sons 🌐 English ⚖ 242 KB 👁 1 views

## Abstract Širáň constructed infinite families of __k__‐crossing‐critical graphs for every __k__⩾3 and Kochol constructed such families of simple graphs for every __k__⩾2. Richter and Thomassen argued that, for any given __k__⩾1 and __r__⩾6, there are only finitely many simple __k__‐crossing‐criti

On Infinite Sum-free Sets of Natural Num
✍ Tomasz łuczak; Tomasz Schoen 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 346 KB

A subset of the natural numbers is k-sum-free if it contains no solutions of the equation x 1 + } } } +x k = y, and strongly k-sum-free when it is l-sum-free for every l=2, ..., k. It is shown that every k-sum-free set with upper density larger than 1Â(k+1) is a subset of a periodic k-sum-free set a

Infinite families of 4-chromatic Grötzsc
✍ Andrey A. Dobrynin; Leonid S. Mel'nikov 📂 Article 📅 2008 🏛 John Wiley and Sons 🌐 English ⚖ 215 KB

## Abstract Let __G__ be a 4‐regular planar graph and suppose that __G__ has a cycle decomposition __S__ (i.e., each edge of __G__ is in exactly one cycle of the decomposition) with every pair of adjacent edges on a face always in different cycles of __S__. Such graphs, called Grötzsch‐Sachs graphs

Note on Infinite Families of Trivalent S
✍ Seymour Lipschutz; Ming-Yao Xu 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 60 KB

A simple undirected graph is said to be semisymmetric if it is regular and edge-transitive but not vertex-transitive. This paper uses the groups PSL(2, p) and PGL(2, p), where p is a prime, to construct two new infinite families of trivalent semisymmetric graphs.

The fractional chromatic number of infin
✍ Imre Leader 📂 Article 📅 1995 🏛 John Wiley and Sons 🌐 English ⚖ 398 KB 👁 1 views

## Abstract The fractional chromatic number of a graph __G__ is the infimum of the total weight that can be assigned to the independent sets of __G__ in such a way that, for each vertex __v__ of __G__, the sum of the weights of the independent sets containing __v__ is at least 1. In this note we g