Combinatorica
On locating minimum feedback vertex sets
Journal of Computer and System Sciences
On the maximum induced forests of a connected cubic graph without triangles
Discrete Mathematics
Discrete Applied Mathematics - Special double volume: interconnection networks
A linear-time algorithm for the weighted feedback vertex problem on interval graphs
Information Processing Letters
Journal of Graph Theory
Almost exact minimum feedback vertex set in meshes and butterflies
Information Processing Letters
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Large induced forests in sparse graphs
Journal of Graph Theory
A note on the integrity of middle graphs
CJCDGCGT'05 Proceedings of the 7th China-Japan conference on Discrete geometry, combinatorics and graph theory
Graph coloring: color sequences and algorithm for color sequence
Proceedings of the 49th Annual Southeast Regional Conference
| Hi-index | 0.04 |
Integrity, a measure of network reliability, is defined as I(G) = minS ⊂ E {|S| + m(G - S)}, where G is a graph with vertex set V and m(G-S) denotes the order of the largest component of G - S. We prove an upper bound of the following form on the integrity of any cubic graph with n vertices: I(G) n + O(√n) Moreover, there exist an infinite family of connected cubic graphs whose integrity satisfies a linear lower bound I(G) βn for some constant β. We provide a value for β, but it is likely not best possible. To prove the upper bound we first solve the following extremal problem. What is the least number of vertices in a cubic graph whose removal results in an acyclic graph? The solution (with a few minor exceptions) is that n/3 vertices suffice and this is best possible.