On approximating the b-chromatic number
نویسندگان
چکیده
We consider the problem of approximating the b-chromatic number of a graph. We show that there is no constant ε > 0 for which this problem can be approximated within a factor of 120/113− ε in polynomial time, unless P = NP. This is the first hardness result for approximating the b-chromatic number.
منابع مشابه
On the Edge-Difference and Edge-Sum Chromatic Sum of the Simple Graphs
For a coloring $c$ of a graph $G$, the edge-difference coloring sum and edge-sum coloring sum with respect to the coloring $c$ are respectively $sum_c D(G)=sum |c(a)-c(b)|$ and $sum_s S(G)=sum (c(a)+c(b))$, where the summations are taken over all edges $abin E(G)$. The edge-difference chromatic sum, denoted by $sum D(G)$, and the edge-sum chromatic sum, denoted by $sum S(G)$, a...
متن کاملZero Knowledge and the Chromatic
We present a new technique, inspired by zero-knowledge proof systems, for proving lower bounds on approximating the chromatic number of a graph. To illustrate this technique we present simple reductions from max-3-coloring and max-3-sat, showing that it is hard to approximate the chromatic number within (N), for some > 0. We then apply our technique in conjunction with the probabilistically che...
متن کاملZero Knowledge and the
We present a new technique, inspired by zero-knowledge proof systems, for proving lower bounds on approximating the chromatic number of a graph. To illustrate this technique we present simple reductions from max-3-coloring and max-3-sat, showing that it is hard to approximate the chromatic number within (N), for some > 0. We then apply our technique in conjunction with the probabilistically che...
متن کاملThe locating-chromatic number for Halin graphs
Let G be a connected graph. Let f be a proper k -coloring of G and Π = (R_1, R_2, . . . , R_k) bean ordered partition of V (G) into color classes. For any vertex v of G, define the color code c_Π(v) of v with respect to Π to be a k -tuple (d(v, R_1), d(v, R_2), . . . , d(v, R_k)), where d(v, R_i) is the min{d(v, x)|x ∈ R_i}. If distinct vertices have distinct color codes, then we call f a locat...
متن کاملAn improved algorithm for approximating the chromatic number of Gn, p
Answering a question of Krivelevich and Vu [12], we present an algorithm for approximating the chromatic number of random graphs Gn,p within a factor of O( √ np/ ln(np)) in polynomial expected time. The algorithm applies to edge probabilities c0/n ≤ p ≤ 0.99, where c0 > 0 is a certain constant.
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:
- Discrete Applied Mathematics
دوره 146 شماره
صفحات -
تاریخ انتشار 2005