TRAVERSING A GRAPH IN GENERAL POSITION

نویسندگان

چکیده

Abstract Let G be a graph. Assume that to each vertex of set vertices $S\subseteq V(G)$ robot is assigned. At stage one can move neighbouring vertex. Then S mobile general position if there exists sequence moves the robots such all are visited while maintaining property at times. The number cardinality largest . We give bounds on and determine exact values for certain common classes graphs, including block rooted products, unicyclic Kneser graphs $K(n,2)$ line complete graphs.

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Traversing the Machining Graph

Zigzag pocket machining (or 2D-milling) plays an important role in the manufacturing industry. The objective is to minimize the number of tool retractions in the zigzag machining path for a given pocket (i.e., a planar domain). We give an optimal linear time dynamic programming algorithm for simply connected pockets, and a linear plus O(1) time optimal algorithm for pockets with h holes. If the...

متن کامل

Traversing the machining graph of a pocket

A simple and linear-time algorithm is presented for solving the problem of traversing a machining graph with minimum retractions encountered in zigzag pocket machining and other applications. This algorithm finds a traversal of the machining graph of a general pocket P with Nh holes, such that the number of retractions in the traversal is no greater than OPT þ Nh þ Nr, where OPT is the (unknown...

متن کامل

Bend-optimal orthogonal graph drawing in the general position model

We consider orthogonal drawings in the general position model, i.e., no two points share a coordinate. The drawings are also required to be bend minimal, i.e., each edge of a drawing in k dimensions has exactly one segment parallel to each coodinate direction that are glued together at k − 1 bends. We provide a precise description of the class of graphs that admit an orthogonal drawing in the g...

متن کامل

The graph theory general position problem on some interconnection networks

Given a graph G, the (graph theory) general position problem is to find the maximum number of vertices such that no three vertices lie on a common geodesic. This graph invariant is called the general position number (gpnumber for short) of G and denoted by gp(G). In this paper, the gp-number is determined for a large class of subgraphs of the infinite grid graph and for the infinite diagonal gr...

متن کامل

Strategic Graph Rewriting Transforming and Traversing Terms with References

Some transformations and many analyses on programs are either difficult or unnatural to express using terms. In particular, analyses that involve type contexts, callor control flow graphs are not easily captured in term rewriting systems. In this paper, we describe an extension to the System S term rewriting system that adds references. We show how references are used for graph rewriting, how w...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Bulletin of The Australian Mathematical Society

سال: 2023

ISSN: ['0004-9727', '1755-1633']

DOI: https://doi.org/10.1017/s0004972723000102