Token Graphs
نویسندگان
چکیده
For a graph G and integer k ≥ 1, we define the token graph Fk(G) to be the graph with vertex set all k-subsets of V (G), where two vertices are adjacent in Fk(G) whenever their symmetric difference is a pair of adjacent vertices in G. Thus vertices of Fk(G) correspond to configurations of k indistinguishable tokens placed at distinct vertices of G, where two configurations are adjacent whenever one configuration can be reached from the other by moving one token along an edge from its current position to an unoccupied vertex. This paper introduces token graphs and studies some of their properties including: connectivity, diameter, cliques, chromatic number, Hamiltonian paths, and Cartesian products of token graphs.
منابع مشابه
Polynomial-Time Algorithms for Sliding Tokens on Cactus Graphs and Block Graphs
Given two independent sets I, J of a graph G, and imagine that a token (coin) is placed at each vertex of I. The Sliding Token problem asks if one could transform I to J via a sequence of elementary steps, where each step requires sliding a token from one vertex to one of its neighbors so that the resulting set of vertices where tokens are placed remains independent. This problem is PSPACE-comp...
متن کاملSliding Token on Bipartite Permutation Graphs
Sliding Token is a natural reconfiguration problem in which vertices of independent sets are iteratively replaced by neighbors. We develop techniques that may be useful in answering the conjecture that Sliding Token is polynomial-time decidable on bipartite graphs. Along the way, we give efficient algorithms for Sliding Token on bipartite permutation and bipartite distance-hereditary graphs.
متن کاملFixed-Parameter Tractability of Token Jumping on Planar Graphs
Suppose that we are given two independent sets I0 and Ir of a graph such that |I0| = |Ir|, and imagine that a token is placed on each vertex in I0. The token jumping problem is to determine whether there exists a sequence of independent sets which transforms I0 into Ir so that each independent set in the sequence results from the previous one by moving exactly one token to another vertex. This ...
متن کاملThe complexity of independent set reconfiguration on bipartite graphs
We settle the complexity of the Independent Set Reconfiguration problem on bipartite graphs under all three commonly studied reconfiguration models. We show that under the token jumping or token addition/removal model the problem is NP-complete. For the token sliding model, we show that the problem remains PSPACE-complete.
متن کاملToken Sliding on Chordal Graphs
Let I be an independent set of a graph G. Imagine that a token is located on any vertex of I . We can now move the tokens of I along the edges of the graph as long as the set of tokens still defines an independent set of G. Given two independent sets I and J , the TOKEN SLIDING problem consists in deciding whether there exists a sequence of independent sets which transforms I into J so that eve...
متن کاملSwapping Colored Tokens on Graphs
We investigate the computational complexity of the following problem. We are given a graph in which each vertex has an initial and a target color. Each pair of adjacent vertices can swap their current colors. Our goal is to perform the minimum number of swaps so that the current and target colors agree at each vertex. When the colors are chosen from {1, 2, . . . , c}, we call this problem c-Col...
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:
- Graphs and Combinatorics
دوره 28 شماره
صفحات -
تاریخ انتشار 2012