منابع مشابه
Zero 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...
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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...
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We prove that the adaptable chromatic number of a graph is at least asymptotic to the square root of the chromatic number. This is best possible. Consider a graph G where each edge of G is assigned a colour from {1, ..., k} (this is not necessarily a proper edge colouring). A k-adapted colouring is an assignment of colours from {1, ..., k} to the vertices of G such that there is no edge with th...
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Let $f$ be a proper $k$-coloring of a connected graph $G$ and $Pi=(V_1,V_2,ldots,V_k)$ be an ordered partition of $V(G)$ into the resulting color classes. For a vertex $v$ of $G$, the color code of $v$ with respect to $Pi$ is defined to be the ordered $k$-tuple $c_{{}_Pi}(v)=(d(v,V_1),d(v,V_2),ldots,d(v,V_k))$, where $d(v,V_i)=min{d(v,x):~xin V_i}, 1leq ileq k$. If distinct...
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We present the rst eecient statistical zero-knowledge protocols to prove statements such as: { A committed number is a prime. { A committed (or revealed) number is the product of two safe primes, i.e., primes p and q such that (p ? 1)=2 and (q ? 1)=2 are prime. { A given integer has large multiplicative order modulo a composite number that consists of two safe prime factors. The main building b...
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ژورنال
عنوان ژورنال: Journal of Computer and System Sciences
سال: 1998
ISSN: 0022-0000
DOI: 10.1006/jcss.1998.1587