Approximations of Independent Set Variants and Hereditary Subset Problems

Approximations via Partitioning

We consider the approximation of weighted maximum subgraph problems by partitioning the input graph into easier subproblems. In particular, we obtain efficient approximations of the weighted independent set problem with performance ratios of O(n(log log n/ log n)) and (∆ + 2)/3, with the latter improving on a ∆/2 ratio of Hochbaum for ∆ ≥ 5. We also obtain a O(n/ log n) performance ratio for va...

Approximations of Weighted Independent Set and Hereditary Subset Problems

The focus of this study is to clarify the approximability of weighted versions of the maximum independent set problem. In particular, we report improved performance ratios in bounded-degree graphs, inductive graphs, and general graphs, as well as for the unweighted problem in sparse graphs. Where possible, the techniques are applied to related hereditary subgraph and subset problem, obtaining r...

Evaluation of MLH1 and MSH2 Gene Mutations in a Subset of Iranian Families with Hereditary Nonpolyposis Colorectal Cancer (HNPCC)

On independent domination numbers of grid and toroidal grid directed graphs

A subset $S$ of vertex set $V(D)$ is an {em indpendent dominating set} of $D$ if $S$ is both an independent and a dominating set of $D$. The {em indpendent domination number}, $i(D)$ is the cardinality of the smallest independent dominating set of $D$. In this paper we calculate the independent domination number of the { em cartesian product} of two {em directed paths} $P_m$ and $P_n$ for arbi...

Global Forcing Number for Maximal Matchings under Graph Operations

Let $S= \{e_1,\,e_2‎, ‎\ldots,\,e_m\}$ be an ordered subset of edges of a connected graph $G$‎. ‎The edge $S$-representation of an edge set $M\subseteq E(G)$ with respect to $S$ is the‎ ‎vector $r_e(M|S) = (d_1,\,d_2,\ldots,\,d_m)$‎, ‎where $d_i=1$ if $e_i\in M$ and $d_i=0$‎ ‎otherwise‎, ‎for each $i\in\{1,\ldots‎ , ‎k\}$‎. ‎We say $S$ is a global forcing set for maximal matchings of $G$‎ ‎if $...