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NonDeterministic Exponential Time has TwoProver Interactive Protocols
"... We determine the exact power of twoprover interactive proof systems introduced by BenOr, Goldwasser, Kilian, and Wigderson (1988). In this system, two allpowerful noncommunicating provers convince a randomizing polynomial time verifier in polynomial time that the input z belongs to the language ..."
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Cited by 416 (37 self)
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are strictly stronger than without, since NEXP # NP. In particular, for the first time, provably polynomial time intractable languages turn out to admit “efficient proof systems’’ since NEXP # P. We show that to prove membership in languages in EXP, the honest provers need the power of EXP only. A consequence
A Query Language and Optimization Techniques for Unstructured Data
, 1996
"... A new kind of data model has recently emerged in which the database is not constrained by a conventional schema. Systems like ACeDB, which has become very popular with biologists, and the recent Tsimmis proposal for data integration organize data in treelike structures whose components can be used ..."
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Cited by 407 (35 self)
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be represented as fixeddepth trees, and on such trees UnQL is equivalent to the relational algebra. The novelty of UnQL consists in its programming constructs for arbitrarily deep data and for cyclic structures. While strictly more powerful than query languages with path expressions like XSQL, UnQL can still
Strictly chordal graphs and . . .
, 2005
"... A phylogeny is the evolutionary history for a set of evolutionarily related species. The development of hereditary trees, or phylogenetic trees, is an important research subject in computational biology. One development approach, motivated by graph theory, constructs a relationship graph based on ev ..."
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. In this thesis, we give a polynomial time algorithm to solve this problem for strictly chordal graphs, a particular subclass of chordal graphs. During the construction of a solution, we examine the problem for tree chordal graphs, and establish new properties for strictly chordal graphs.
On Powers of Chordal Graphs And Their Colorings
 Congr. Numer
, 2000
"... The kth power of a graph G is a graph on the same vertex set as G, where a pair of vertices is connected by an edge if they are of distance at most k in G. We study the structure of powers of chordal graphs and the complexity of coloring them. We start by giving new and constructive proofs of t ..."
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Cited by 24 (1 self)
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The kth power of a graph G is a graph on the same vertex set as G, where a pair of vertices is connected by an edge if they are of distance at most k in G. We study the structure of powers of chordal graphs and the complexity of coloring them. We start by giving new and constructive proofs
Coloring Powers of Chordal Graphs
, 2003
"... We prove that the kth power G of a chordal graph G with maximum degree is O( )degenerated for even values of k and O( )degenerated for odd ones. In particular, this bounds the chromatic number (G ). The bound proven for odd values of k is the best possible. Another consequence ..."
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Cited by 18 (6 self)
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We prove that the kth power G of a chordal graph G with maximum degree is O( )degenerated for even values of k and O( )degenerated for odd ones. In particular, this bounds the chromatic number (G ). The bound proven for odd values of k is the best possible. Another consequence
On Leaf Powers
"... For an integer k, a tree T is a kleaf root of a finite simple undirected graph G = (V, E) if the set of leaves of T is the vertex set V of G and for any two vertices x, y ∈ V, x ̸ = y, xy ∈ E if and only if the distance of x and y in T is at most k. Then graph G is a kleaf power if it has a kleaf ..."
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Cited by 15 (2 self)
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discuss the relationship between leaf powers and strongly chordal graphs as well as fixed tolerance NeST graphs, describe some subclasses of leaf powers, give the complete inclusion structure of kleaf power classes, and describe various characterizations of 3and 4leaf powers, as well as of distance
Bipartite Powers of kchordal Graphs
, 2013
"... Let k be an integer and k ≥ 3. A graph G is kchordal if G does not have an induced cycle of length greater than k. From the definition it is clear that 3chordal graphs are precisely the class of chordal graphs. Duchet proved that, for every positive integer m, if G m is chordal then so is G m+2. B ..."
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. Brandstädt et al. in [Andreas Brandstädt, Van Bang Le, and Thomas Szymczak. Duchettype theorems for powers of HHDfree graphs. Discrete Mathematics, 177(13):916, 1997.] showed that if G m is kchordal, then so is G m+2. Powering a bipartite graph does not preserve its bipartitedness. In order to preserve
On Chordal Graphs and their Chromatic Polynomials
 Mathematica Scandinavica
"... We derive a formula for the chromatic polynomial of a chordal or a triangulated graph in terms of its maximal cliques. As a corollary we obtain a way to write down an explicit formula for the chromatic polynomial for an arbitrary power of a graph which belongs to any given class of chordal graphs th ..."
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Cited by 1 (1 self)
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We derive a formula for the chromatic polynomial of a chordal or a triangulated graph in terms of its maximal cliques. As a corollary we obtain a way to write down an explicit formula for the chromatic polynomial for an arbitrary power of a graph which belongs to any given class of chordal graphs
On injective colourings of chordal graphs
 Lecture Notes in Computer Sci
"... Abstract. We show that one can compute the injective chromatic number of a chordal graph G at least as efficiently as one can compute the chromatic number of (G−B)2, where B are the bridges of G. In particular, it follows that for strongly chordal graphs and socalled power chordal graphs the inje ..."
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Cited by 1 (0 self)
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Abstract. We show that one can compute the injective chromatic number of a chordal graph G at least as efficiently as one can compute the chromatic number of (G−B)2, where B are the bridges of G. In particular, it follows that for strongly chordal graphs and socalled power chordal graphs
5th phylogenetic root construction for strictly chordal graphs
 In Proc. 16th ISAAC, volume 3827 of LNCS
, 2005
"... Abstract. Reconstruction of an evolutionary history for a set of organisms is an important research subject in computational biology. One approach motivated by graph theory constructs a relationship graph based on pairwise evolutionary closeness. The approach builds a tree representation equivalent ..."
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Cited by 4 (1 self)
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if k ≥ 5. We present a polynomial time algorithm for strictly chordal relationship graphs if k = 5.
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