𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Largest bipartite subgraphs in triangle-free graphs with maximum degree three

✍ Scribed by J. A. Bondy; S. C. Locke

Publisher
John Wiley and Sons
Year
1986
Tongue
English
Weight
977 KB
Volume
10
Category
Article
ISSN
0364-9024

No coin nor oath required. For personal study only.

✦ Synopsis

Let G be a triangle-free, loopless graph with maximum degree three. We display a polynomi$ algorithm which returns a bipartite subgraph of G containing at least 5 of the edges of G. Furthermore, we characterize the dodecahedron and the Petersen graph as the only 3-regular, triangle-free, loopless, connected graphs for which no bipartite subgraph has more than this proportion.

πŸ“œ SIMILAR VOLUMES

Size and independence in triangle-free g
Size and independence in triangle-free graphs with maximum degree three
✍ Kathryn Fraughnaugh Jones πŸ“‚ Article πŸ“… 1990 πŸ› John Wiley and Sons 🌐 English βš– 549 KB

## Abstract Let __C__ be the class of triangle‐free graphs with maximum degree at most three. A lower bound for the number of edges in a graph of __C__ is derived in terms of the number of vertices and the independence. Several classes of graphs for which this bound is attained are given. As coroll

Edge density and independence ratio in t
Edge density and independence ratio in triangle-free graphs with maximum degree three
✍ Jerrold Griggs; Owen Murphy πŸ“‚ Article πŸ“… 1996 πŸ› Elsevier Science 🌐 English βš– 548 KB

A simple polynomial-time algorithm is presented which computes independent sets of guaranteed size in connected triangle-free noncubic graphs with maximum degree 3. Let nand m denote the number of vertices and edges, respectively, and let c '= m/n denote the edge density where c < 3/2. The algorithm