𝔖 Bobbio Scriptorium
✦   LIBER   ✦

The edge reconstruction of hamiltonian graphs

✍ Scribed by L. Pyber

Publisher
John Wiley and Sons
Year
1990
Tongue
English
Weight
305 KB
Volume
14
Category
Article
ISSN
0364-9024

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

If a graph G on n vertices contains a Hamiltonian path, then G is reconstructible from its edge‐deleted subgraphs for n sufficiently large.

📜 SIMILAR VOLUMES

Edge-reconstruction of 4-connected plana
Edge-reconstruction of 4-connected planar graphs
✍ S. Fiorini; J. Lauri 📂 Article 📅 1982 🏛 John Wiley and Sons 🌐 English ⚖ 482 KB 👁 2 views

## Abstract The object of this paper is to show that 4‐connected planar graphs are uniquely determined from their collection of edge‐deleted subgraphs.

Claw-free graphs are edge reconstructibl
Claw-free graphs are edge reconstructible
✍ M. N. Ellingham; L. Pyber; Xingxing Yu 📂 Article 📅 1988 🏛 John Wiley and Sons 🌐 English ⚖ 318 KB 👁 1 views

The Edge Reconstruction Conjecture states that all graphs with at least four edges are determined by their edge-deleted subgraphs. We prove that this is true for claw-free graphs, those graphs with no induced subgraph isomorphic to K,,3. This includes line graphs as a special case.

Eulerian subgraphs in 3-edge-connected g
Eulerian subgraphs in 3-edge-connected graphs and Hamiltonian line graphs
✍ Zhi-Hong Chen; Hong-Jian Lai; Xiangwen Li; Deying Li; Jinzhong Mao 📂 Article 📅 2003 🏛 John Wiley and Sons 🌐 English ⚖ 111 KB

## Abstract In this paper, we show that if __G__ is a 3‐edge‐connected graph with $S \subseteq V(G)$ and $|S| \le 12$, then either __G__ has an Eulerian subgraph __H__ such that $S \subseteq V(H)$, or __G__ can be contracted to the Petersen graph in such a way that the preimage of each vertex of th

Hamiltonian weights and unique 3-edge-co
Hamiltonian weights and unique 3-edge-colorings of cubic graphs
✍ Cun-Quan Zhang 📂 Article 📅 1995 🏛 John Wiley and Sons 🌐 English ⚖ 402 KB

## Abstract A (1,2)‐eulerian weight __w__ of a grph is hamiltonian if every faithful cover of __w__ is a set of two Hamilton circuits. Let __G__ be a 3‐connected cubic graph containing no subdivition of the Petersen graph. We prove that if __G__ admits a hamiltonian weight then __G__ is uniquely 3‐

Some 3-connected 4-edge-critical non-Ham
Some 3-connected 4-edge-critical non-Hamiltonian graphs
✍ Yang Yuansheng; Zhao Chengye; Lin Xiaohui; Jiang Yongsong; Hao Xin 📂 Article 📅 2005 🏛 John Wiley and Sons 🌐 English ⚖ 79 KB 👁 1 views

## Abstract Let γ(__G__) be the domination number of graph __G__, thus a graph __G__ is __k__‐edge‐critical if γ (__G__) = k, and for every nonadjacent pair of vertices __u__ and υ, γ(__G__ + __u__υ) = k−1. In Chapter 16 of the book “Domination in Graphs—Advanced Topics,” D. Sumner cites a conjectu