✦ LIBER ✦

Locally K3,3 or Petersen graphs

✍ Scribed by A. Blokhuis; A.E. Brouwer

Publisher: Elsevier Science
Year: 1992
Tongue: English
Weight: 617 KB
Volume: 106-107
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(92)90529-o

No coin nor oath required. For personal study only.

✦ Synopsis

Blokhuis,

A. and A.E. Brouwer, Locally K,,, or Petersen graphs, Discrete Mathematics 106/107 (1992) 53-60.

We determine all graphs with the property that each of its local graphs (point neighbourhoods) is isomorphic to either the Petersen graph or the complete bipartite graph K,,,. This answers a question of J.I. Hall.

📜 SIMILAR VOLUMES

Locally petersen graphs

✍ J. I. Hall 📂 Article 📅 1980 🏛 John Wiley and Sons 🌐 English ⚖ 684 KB

## Abstract A graph Γ is locally Petersen if, for each point __t__ of Γ, the graph induced by Γ on all points adjacent to __t__ is isomorphic to the Petersen graph. We prove that there are exactly three isomorphism classes of connected, locally Petersen graphs and further characterize these graphs

Connected, locally 2-connected, K1,3-fre

Connected, locally 2-connected, K1,3-free graphs are panconnected

✍ S. V. Kanetkar; P. R. Rao 📂 Article 📅 1984 🏛 John Wiley and Sons 🌐 English ⚖ 288 KB 👁 1 views

## Abstract A graph __G__ is locally __n__‐connected, __n__ ≥ 1, if the subgraph induced by the neighborhood of each vertex is __n__‐connected. We prove that every connected, locally 2‐connected graph containing no induced subgraph isomorphic to __K__~1,3~ is panconnected.

Hamiltonian circuits in N2-locally conne

Hamiltonian circuits in N2-locally connected K1,3-free graphs

✍ ZdeněK Ryjáček 📂 Article 📅 1990 🏛 John Wiley and Sons 🌐 English ⚖ 407 KB 👁 1 views

## Abstract There are many results concerned with the hamiltonicity of __K__~1,3~‐free graphs. In the paper we show that one of the sufficient conditions for the __K__~1,3~‐free graph to be Hamiltonian can be improved using the concept of second‐type vertex neighborhood. The paper is concluded with

Nowhere-zero 3-flows in locally connecte

Nowhere-zero 3-flows in locally connected graphs

✍ Hong-Jian Lai 📂 Article 📅 2003 🏛 John Wiley and Sons 🌐 English ⚖ 91 KB 👁 1 views

## Abstract Let __G__ be a graph. For each vertex __v__ ∈__V__(__G__), __N~v~__ denotes the subgraph induces by the vertices adjacent to __v__ in __G__. The graph __G__ is locally __k__‐edge‐connected if for each vertex __v__ ∈__V__(__G__), __N~v~__ is __k__‐edge‐connected. In this paper we study t

A necessary and sufficient condition for

A necessary and sufficient condition for connected, locally k-connected k1,3-free graphs to be k-hamiltonian

✍ Zhou Huai-Lu 📂 Article 📅 1989 🏛 John Wiley and Sons 🌐 English ⚖ 272 KB 👁 2 views

We prove the following conjecture of Broersma and Veldman: A connected, locally k-connected K,,-free graph is k-hamiltonian if and only if it is (k + 2)-connected ( k L 1). We use [ 11 for basic terminology and notation, and consider simple graphs only. Let G be a graph. By V(G) and E(G) we denote,

Characterization of k-variegated graphs,

Characterization of k-variegated graphs, k ⩾ 3

✍ Medha Javdekar 📂 Article 📅 1980 🏛 Elsevier Science 🌐 English ⚖ 415 KB