✦ LIBER ✦

Random Planar Graphs with Bounds on the Maximum and Minimum Degrees

✍ Scribed by Chris Dowden

Publisher: Springer Japan
Year: 2010
Tongue: English
Weight: 452 KB
Volume: 27
Category: Article
ISSN: 0911-0119
DOI: 10.1007/s00373-010-0960-7

No coin nor oath required. For personal study only.

📜 SIMILAR VOLUMES

On the fixed edge of planar graphs with

On the fixed edge of planar graphs with minimum degree five

✍ Baogang Xu; Hongbing Fan 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 207 KB

An edge e of a finite and simple graph G is called a fixed edge of G if G -e + e' ~G implies e' = e. In this paper, we show that planar graphs with minimum degree 5 contain fixed edges, from which we prove that a class of planar graphs with minimum degree one is edge reconstructible.

On Induced Ramsey Numbers for Graphs wit

On Induced Ramsey Numbers for Graphs with Bounded Maximum Degree

✍ Tomasz Łuczak; Vojtěch Rödl 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 435 KB

For graphs G and H we write G wÄ ind H if every 2-edge colouring of G yields an induced monochromatic copy of H. The induced Ramsey number for H is defined as r ind (H)=min[ |V(G)|: G wÄ ind H]. We show that for every d 1 there exists an absolute constant c d such that r ind (H n, d ) n cd for every

Realizability of p-point graphs with pre

Realizability of p-point graphs with prescribed minimum degree, maximum degree, and line connectivity

✍ F. T. Boesch; C. L. Suffel 📂 Article 📅 1980 🏛 John Wiley and Sons 🌐 English ⚖ 316 KB

## Abstract It is well known that certain graph‐theoretic extremal questions play a central role in the study of communication network vulnerability. Herein we consider a generalization of some of the classical results in this area. We define a (__p__, Δ, δ, λ) graph as a graph having __p__ points,

Graph decomposition with constraints on

Graph decomposition with constraints on the minimum degree

✍ John Sheehan 📂 Article 📅 1988 🏛 Elsevier Science 🌐 English ⚖ 888 KB

Let G be a finite simple graph on n vertices with minimum degree 6(G) 3 6 (n = 6 (mod 2)). Let max(k, G) denote the set of all k-subsets A E V(G) such that the number of edges in the induced subgraph (A) is a maximum. We prove that for some i E (0, 1.2, . . . ). Analogous edge density constraints, r

On Light Edges and Triangles in Planar G

On Light Edges and Triangles in Planar Graphs of Minimum Degree Five

✍ Oleg V. Borodin; Daniel P. Sanders 📂 Article 📅 2006 🏛 John Wiley and Sons 🌐 English ⚖ 342 KB 👁 1 views

## Abstract This paper presents two tight inequalities for planar graphs of minimum degree five. An edge or face of a plane graph is light if the sum of the degrees of the vertices incident with it is small. A light edge inequality is presented which shows that planar graphs of minimum degree five

Graph decomposition with constraints on

Graph decomposition with constraints on the connectivity and minimum degree

✍ Carsten Thomassen 📂 Article 📅 1983 🏛 John Wiley and Sons 🌐 English ⚖ 145 KB 👁 1 views

## Abstract For each pair __s,t__ of natural numbers there exist natural numbers __f(s,t)__ and __g(s,t)__ such that the vertex set of each graph of connectivity at least __f(s,t)__ (respectively minimum degree at least __g(s,t))__ has a decomposition into sets which induce subgraphs of connectivit