The kk-Dominating Graph

Given a graph $G$, the $k$-dominating graph of $G$, $D_k(G)$, is defined to be the graph whose vertices correspond to the dominating sets of $G$ that have cardinality at most $k$. Two vertices in $D_k(G)$ are adjacent if and only if the corresponding dominating sets of $G$ differ by either adding or deleting a single vertex. The graph $D_k(G)$ aids in studying the reconfiguration problem for dominating sets. In particular, one dominating set can be reconfigured to another by a sequence of single vertex additions and deletions, such that the intermediate set of vertices at each step is a dominating set if and only if they are in the same connected component of $D_k(G)$. In this paper we give conditions that ensure $D_k(G)$ is connected.Comment: 2 figure, The final publication is available at http://link.springer.co

Hajós' conjecture and small cycle double covers of planar graphs

AbstractWe prove that every simple even planar graph on n vertices has a partition of its edge set into at most ⌊(n - 1)/2⌋ cycles. A previous proof of this result was given by Tao, but is incomplete, and we provide here a somewhat different proof. We also discuss the connection between this result and the Small Cycle Double Cover Conjecture

Community Health Information Resource Guide: Volume 1 - Data

This resource guide contains useful information for those who would like to use data to assess the health status of an Indiana community. Targeted users include local organizations such as county health departments and community health coalitions. Being able to access and use relevant data and information resources is a common hurdle for those interested in assessing and advancing community health. As a result of this need and at the request of the Community Advisory Council of the Community Health Engagement Program, we developed this resource guide to assist individuals, organizations, and coalitions in Indiana in identifying appropriate resources that guide their community health research and evaluation activities. The term “data” is used in this volume in reference to both data and information sources. While data consist of raw facts and figures, information is formed by analyzing the data and applying knowledge to it so that the findings are more meaningful and valuable to the community. The benefit of using data is that you can often manipulate it for your specific purposes. The benefit of using information sources is that the work of generating meaning from the data might already have been done, while a potential downside is that the available sources might not answer your specific questions. There are diverse sources of data that can be used as a basis for community health evaluation and decision making. Those looking to use data must consider multiple factors before determining the appropriate data to seek and use.Community Health Engagement Program (CHEP) Indiana Clinical and Translational Sciences Institute (Indiana CTSI

Dynamic and Self-stabilizing Distributed Matching

Self-stabilization is a unified model of fault tolerance. A self-stabilizing system can recover from an arbitrary transient fault without re-initialization. Self-stabilization is a particularly valuable attribute of distributed systems since they are tipically prone to various faults and dynamic changes. In several distributed applications, pairing of processors connected in a network can be viewed as a matching of the underlying graph of the network. A self-stabilizing matching algorithm can be used to build fault tolerant pairing of clients and servers connected in a network. First contribution of this report is an efficient, dynamic and self-stabilizing mazimal matching algorithm for arbitrary anonymous networks. The algorithm implements a locally distinct label generation technique that can be used by other applications. The second contribution of this report is a dynamic and self-stabilizing maximum matching alrogithm for arbitrary biparite networks. This is the first distributed amximum matching algorithm for networks containing cycles.We are currently acquiring citations for the work deposited into this collection. We recognize the distribution rights of this item may have been assigned to another entity, other than the author(s) of the work.If you can provide the citation for this work or you think you own the distribution rights to this work please contact the Institutional Repository Administrator at [email protected]