On the Achromatic Number of Hypercubes
نویسنده
چکیده
The achromatic number of a nite graph G, (G), is the maximum number of independent sets into which the vertex set may be partitioned, so that between any two parts there is at least one edge. For an m-dimensional hypercube P m 2 we prove: There exist constants 0 < c 1 < c 2 , independent of m, such that
منابع مشابه
Time and Bit Optimal Broadcasting on Anonymous Unoriented Hypercubes
We consider broadcasting on asynchronous anonymous totally unoriented N node hypercubes. First we generalize a technique, introduced in [3], for partial broadcasting and orientation. Using this technique we develop a broadcasting algorithm on unoriented hypercubes that uses only linear number of bits and runs in optimal time. This gives a positive answer to the question raised in [7] whether O(...
متن کاملConcerning the achromatic number of graphs
The achromatic number of a graph G is the largest number of colors that can be assigned to the vertices of G so that (i) adjacent vertices are assigned different colors, and (ii) any two different colors are assigned to some pair of adjacent vertices. We study the achromatic number from the point of view of computational complexity. We show that, for each fixed integer n, there is an algorithm ...
متن کاملThe achromatic number of Kneser graphs
The achromatic number α of a graph is the largest number of colors that can be assigned to its vertices such that adjacent vertices have different color and every pair of different colors appears on the end vertices of some edge. We estimate the achromatic number of Kneser graphs K(n, k) and determine α(K(n, k)) for some values of n and k. Furthermore, we study the achromatic number of some geo...
متن کاملThe domination number of exchanged hypercubes
Exchanged hypercubes [Loh et al., IEEE Transactions on Parallel and Distributed Systems 16 (2005) 866–874] are spanning subgraphs of hypercubes with about one half of their edges but still with many desirable properties of hypercubes. Lower and upper bounds on the domination number of exchanged hypercubes are proved which in particular imply that γ(EH(2, t)) = 2 holds for any t ≥ 2. Using Hammi...
متن کاملA ug 2 01 7 On the number of proper paths between vertices in edge - colored hypercubes
Given an integer 1 ≤ j < n, define the (j)-coloring of a n-dimensional hypercube Hn to be the 2-coloring of the edges of Hn in which all edges in dimension i, 1 ≤ i ≤ j, have color 1 and all other edges have color 2. Cheng et al. [Proper distance in edge-colored hypercubes, Applied Mathematics and Computation 313 (2017) 384-391.] determined the number of distinct shortest properly colored paths...
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:
- J. Comb. Theory, Ser. B
دوره 79 شماره
صفحات -
تاریخ انتشار 2000