Faster computation of maximum independent set and parameterized vertex cover for graphs with maximum degree 3

On the Independence Number of Graphs with Maximum Degree 3

Let G be an undirected graph with maximum degree at most 3 such that G does not contain any of the three graphs shown in Figure 1 as a subgraph. We prove that the independence number of G is at least n(G)/3 + nt(G)/42, where n(G) is the number of vertices in G and nt(G) is the number of nontriangle vertices in G. This bound is tight as implied by the wellknown tight lower bound of 5n(G)/14 on t...

Maximum Independent Set in Graphs of Average Degree at Most Three in O(1.08537n){\mathcal O}(1.08537^n)

We show that Maximum Independent Set on connected graphs of average degree at most three can be solved in O(1.08537) time and linear space. This improves previous results on graphs of maximum degree three, as our connectivity requirement only functions to ensure that each connected component has average degree at most three. We link this result to exact algorithms of Maximum Independent Set on ...

Faster Computation of the Maximum Dissociation Set and Minimum 3-Path Vertex Cover in Graphs

Hardness of Approximating Problems on Cubic Graphs

Four fundamental graph problems, Minimum vertex cover, Maximum independent set, Minimum dominating set and Maximum cut, are shown to be APX-complete even for cubic graphs. This means that unless P=NP these problems do not admit any polynomial time approximation scheme on input graphs of degree bounded by three.

On reverse degree distance of unicyclic graphs

The reverse degree distance of a connected graph $G$ is defined in discrete mathematical chemistry as [ r (G)=2(n-1)md-sum_{uin V(G)}d_G(u)D_G(u), ] where $n$, $m$ and $d$ are the number of vertices, the number of edges and the diameter of $G$, respectively, $d_G(u)$ is the degree of vertex $u$, $D_G(u)$ is the sum of distance between vertex $u$ and all other vertices of $G$, and $V(G)$ is the...