Compound Node-Kayles on paths
نویسندگان
چکیده
In his celebrated book On Number and Games (Academic Press, New-York, 1976), J. H. Conway introduced twelve versions of compound games. We analyze these twelve versions for the Node-Kayles game on paths. For usual disjunctive compound, Node-Kayles has been solved for a long time under normal play, while it is still unsolved under misère play. We thus focus on the ten remaining versions, leaving only one of them unsolved.
منابع مشابه
Sink Location Service Based on Fano Plane in Wireless Sensor Networks
Sink location is considered as a basic service in geographic routing in wireless sensor networks. Obtaining the location of sink node by source node using an efficient method with low complexity has always been a challenging issue in research. In this paper, a sink location algorithm based on Fano plane is proposed. The research challenge is how to ensure the intersection of two SLQ (Location Q...
متن کاملA generalization of Arc-Kayles
The game Arc-Kayles is played on an undirected graph with two players taking turns deleting an edge and its endpoints from the graph. We study a generalization of this game, Weighted Arc Kayles (WAK for short), played on graphs with counters on the vertices. The two players alternate choosing an edge and removing one counter on both endpoints. An edge can no longer be selected if any of its end...
متن کاملKayles and Nimbers
Kayles is a combinatorial game on graphs. Two players select alternatingly a vertex from a given graph G a chosen vertex may not be adjacent or equal to an already chosen vertex. The last player that can select a vertex wins the game. The problem to determine which player has a winning strategy is known to be PSPACE-complete. Because of certain characteristics of the Kayles game, it can be anal...
متن کاملExact Algorithms for Kayles
In the game of Kayles, two players select alternatingly a vertex from a given graph G, but may never choose a vertex that is adjacent or equal to an already chosen vertex. The last player that can select a vertex wins the game. In this paper, we give an exact algorithm to determine which player has a winning strategy in this game. To analyse the running time of the algorithm, we introduce the n...
متن کاملMultipath Node-Disjoint Routing with Backup List Based on the AODV Protocol
In recent years, routing has been the most focused area in ad hoc networks research. On-demand routing in particular, is widely developed in bandwidth constrained mobile wireless ad hoc networks because of its effectiveness and efficiency. Most proposed on-demand routing protocols are built and relied on single route for each data session. Whenever there is a link disconnection on the active ro...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Theor. Comput. Sci.
دوره 410 شماره
صفحات -
تاریخ انتشار 2009