Hong-Gwa Yeh

Some results on the target set selection problem

In this paper we consider a fundamental problem in the area of viral marketing, called Target Set Selection problem. We study the problem when the underlying graph is a block-cactus graph, a chordal graph or a Hamming graph. We show that if G is a block-cactus graph, then the Target Set Selection problem can be solved in linear time, which generalizes Chen’s result (Discrete Math. 23:1400–1415, 2009) for trees, and the time complexity is much better than the algorithm in Ben-Zwi et al. (Discrete Optim., 2010) (for bounded treewidth graphs) when restricted to block-cactus graphs. We show that if the underlying graph G is a chordal graph with thresholds θ(v)≤2 for each vertex v in G, then the problem can be solved in linear time. For a Hamming graph G having thresholds θ(v)=2 for each vertex v of G, we precisely determine an optimal target set S for (G,θ). These results partially answer an open problem raised by Dreyer and Roberts (Discrete Appl. Math. 157:1615–1627, 2009).

Domination in distance-hereditary graphs

The domination problem and its variants have been extensively studied in the literature. In this paper we investigate the domination problem in distance-hereditary graphs. In particular, we give a linear-time algorithm for the domination problem in distance-hereditary graphs by a labeling approach. We actually solve a more general problem, called the L-domination problem, which also includes the total domination problem as a special case.

Weighted connected domination and Steiner trees in distance-hereditary graphs

Abstract Distance-hereditary graphs are graphs in which every two vertices have the same distance in every connected induced subgraph containing them. This paper studies distance-hereditary graphs from an algorithmic viewpoint. In particular, we present linear-time algorithms for finding a minimum weighted connected dominating set and a minimum vertex-weighted Steiner tree in a distance-hereditary graph. Both problems are N P -complete in general graphs.

Target Set Selection Problem for Honeycomb Networks

Let

Centers and medians of distance-hereditary graphs

G

4-Colorable 6-regular toroidal graphs

be a graph with a threshold function

On the fractional chromatic number, the chromatic number, and graph products

\theta:V(G)\rightarrow \mathbb{N}

Weighted connected k-domination and weighted k-dominating clique in distance-hereditary graphs

such that

Sortabilities of Partition Properties

1\leq \theta(v)\leq d_G(v)

k -Subdomination in graphs

for every vertex