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Colorful paths in vertex coloring of graphs
"... A colorful path in a graph G is a path with χ(G) vertices whose colors are different. A vcolorful path is such a path, starting from v. Let G 6 = C7 be a connected graph with maximum degree ∆(G). We show that there exists a (∆(G)+1)coloring of G with a vcolorful path for every v ∈ V (G). We also ..."
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Cited by 4 (0 self)
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A colorful path in a graph G is a path with χ(G) vertices whose colors are different. A vcolorful path is such a path, starting from v. Let G 6 = C7 be a connected graph with maximum degree ∆(G). We show that there exists a (∆(G)+1)coloring of G with a vcolorful path for every v ∈ V (G). We
Pathrelated vertex colorings of graphs
"... We investigate algorithms for a frequency assignment problem in cellular networks. The problem can be modeled as a special coloring problem for graphs. Base stations are the vertices, ranges are the paths in the graph, and colors (frequencies) must be assigned to vertices following the conflictfree ..."
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We investigate algorithms for a frequency assignment problem in cellular networks. The problem can be modeled as a special coloring problem for graphs. Base stations are the vertices, ranges are the paths in the graph, and colors (frequencies) must be assigned to vertices following the conflict
Vertex distinguishing colorings of graphs with
 G) = 2, Discrete Mathematics 252(2002)17 ∼ 29
"... In a paper by Burris and Schelp [3], a conjecture was made concerning the number of colors χ′s(G) required to proper edgecolor G so that each vertex has a distinct set of colors incident to it. We consider the case when ∆(G) = 2, so that G is a union of paths and cycles. In particular we find the ..."
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Cited by 10 (2 self)
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In a paper by Burris and Schelp [3], a conjecture was made concerning the number of colors χ′s(G) required to proper edgecolor G so that each vertex has a distinct set of colors incident to it. We consider the case when ∆(G) = 2, so that G is a union of paths and cycles. In particular we find
A new approach to the maximum flow problem
 JOURNAL OF THE ACM
, 1988
"... All previously known efficient maximumflow algorithms work by finding augmenting paths, either one path at a time (as in the original Ford and Fulkerson algorithm) or all shortestlength augmenting paths at once (using the layered network approach of Dinic). An alternative method based on the pre ..."
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Cited by 672 (33 self)
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to be shortest paths. The algorithm and its analysis are simple and intuitive, yet the algorithm runs as fast as any other known method on dense. graphs, achieving an O(n³) time bound on an nvertex graph. By incorporating the dynamic tree data structure of Sleator and Tarjan, we obtain a version
A New Method for Solving Hard Satisfiability Problems
 AAAI
, 1992
"... We introduce a greedy local search procedure called GSAT for solving propositional satisfiability problems. Our experiments show that this procedure can be used to solve hard, randomly generated problems that are an order of magnitude larger than those that can be handled by more traditional approac ..."
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Cited by 730 (21 self)
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approaches such as the DavisPutnam procedure or resolution. We also show that GSAT can solve structured satisfiability problems quickly. In particular, we solve encodings of graph coloring problems, Nqueens, and Boolean induction. General application strategies and limitations of the approach are also
Property Testing and its connection to Learning and Approximation
"... We study the question of determining whether an unknown function has a particular property or is fflfar from any function with that property. A property testing algorithm is given a sample of the value of the function on instances drawn according to some distribution, and possibly may query the fun ..."
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Cited by 475 (67 self)
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the function on instances of its choice. First, we establish some connections between property testing and problems in learning theory. Next, we focus on testing graph properties, and devise algorithms to test whether a graph has properties such as being kcolorable or having a aeclique (clique of density ae
Where the REALLY Hard Problems Are
 IN J. MYLOPOULOS AND R. REITER (EDS.), PROCEEDINGS OF 12TH INTERNATIONAL JOINT CONFERENCE ON AI (IJCAI91),VOLUME 1
, 1991
"... It is well known that for many NPcomplete problems, such as KSat, etc., typical cases are easy to solve; so that computationally hard cases must be rare (assuming P != NP). This paper shows that NPcomplete problems can be summarized by at least one "order parameter", and that the hard p ..."
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Cited by 683 (1 self)
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problems occur at a critical value of such a parameter. This critical value separates two regions of characteristically different properties. For example, for Kcolorability, the critical value separates overconstrained from underconstrained random graphs, and it marks the value at which the probability
Rainbow paths with prescribed ends
 Electron. J. Combin
, 2011
"... It was conjectured in [S. Akbari, F. Khaghanpoor, and S. Moazzeni. Colorful paths in vertex coloring of graphs. Preprint] that, if G is a connected graph distinct from C7, then there is a χ(G)coloring of G in which every vertex v ∈ V (G) is an initial vertex of a path P with χ(G) vertices whose col ..."
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Cited by 3 (1 self)
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It was conjectured in [S. Akbari, F. Khaghanpoor, and S. Moazzeni. Colorful paths in vertex coloring of graphs. Preprint] that, if G is a connected graph distinct from C7, then there is a χ(G)coloring of G in which every vertex v ∈ V (G) is an initial vertex of a path P with χ(G) vertices whose
Tabu Search  Part I
, 1989
"... This paper presents the fundamental principles underlying tabu search as a strategy for combinatorial optimization problems. Tabu search has achieved impressive practical successes in applications ranging from scheduling and computer channel balancing to cluster analysis and space planning, and more ..."
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Cited by 680 (11 self)
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, and more recently has demonstrated its value in treating classical problems such as the traveling salesman and graph coloring problems. Nevertheless, the approach is still in its infancy, and a good deal remains to be discovered about its most effective forms of implementation and about the range
On the pathavoidance vertexcoloring game
 In preparation
"... For any graph F and any integer r ≥ 2, the online vertexRamsey density of F and r, denoted m ∗ (F, r), is a parameter defined via a deterministic twoplayer Ramseytype game (Painter vs. Builder). This parameter was introduced in a recent paper [4], where it was shown that the online vertexRamsey ..."
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Cited by 2 (2 self)
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For any graph F and any integer r ≥ 2, the online vertexRamsey density of F and r, denoted m ∗ (F, r), is a parameter defined via a deterministic twoplayer Ramseytype game (Painter vs. Builder). This parameter was introduced in a recent paper [4], where it was shown that the online vertex
Results 1  10
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