✦ LIBER ✦

On 3-connected hamiltonian line graphs

✍ Scribed by Ye Chen; Suohai Fan; Hong-Jian Lai

Book ID: 113567623
Publisher: Elsevier Science
Year: 2012
Tongue: English
Weight: 223 KB
Volume: 312
Category: Article
ISSN: 0012-365X
DOI: 10.1016/j.disc.2012.02.024

No coin nor oath required. For personal study only.

📜 SIMILAR VOLUMES

On hamiltonian line graphs and connectiv

On hamiltonian line graphs and connectivity

✍ Siming Zhan 📂 Article 📅 1991 🏛 Elsevier Science 🌐 English ⚖ 444 KB

A well-known conjecture of Thomassen says that every 4-connected line graph is hamiltonian. In this paper we prove that every 7-connected line graph is hamiltonian-connected. For line graph, C. Thomassen [l] made the following conjecture. Conjecture. Every 4-connected line graph is hamiltonian.

Hamiltonian connected hourglass free lin

Hamiltonian connected hourglass free line graphs

✍ Li Dengxin; Hong-Jian Lai; Yehong Shao; Mingquan Zhan 📂 Article 📅 2008 🏛 Elsevier Science 🌐 English ⚖ 148 KB

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

On hamiltonian-connected graphs

✍ Ronald J. Gould; Xingxing Yu 📂 Article 📅 1994 🏛 John Wiley and Sons 🌐 English ⚖ 735 KB

## Abstract One of the most fundamental results concerning paths in graphs is due to Ore: In a graph __G__, if deg __x__ + deg __y__ ≧ |__V__(__G__)| + 1 for all pairs of nonadjacent vertices __x, y__ ≅ __V__(__G__), then __G__ is hamiltonian‐connected. We generalize this result using set degrees.

3-Connected line graphs of triangular gr

3-Connected line graphs of triangular graphs are panconnected and 1-hamiltonian

✍ H. J. Broersma; H. J. Veldman 📂 Article 📅 1987 🏛 John Wiley and Sons 🌐 English ⚖ 368 KB 👁 1 views

A graph is k-triangular if each edge is in at least k triangles. Triangular is a synonym for l-triangular. It is shown that the line graph of a triangular graph of order at least 4 is panconnected if and only if it is 3-connected. Furthermore, the line graph of a k-triangular graph is k-harniltonian

Every 3-connected, essentially 11-connec

Every 3-connected, essentially 11-connected line graph is Hamiltonian

✍ Hong-Jian Lai; Yehong Shao; Hehui Wu; Ju Zhou 📂 Article 📅 2006 🏛 Elsevier Science 🌐 English ⚖ 89 KB