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Balanced Paths in Colored Graphs
, 2009
"... Abstract. We consider finite graphs whose edges are labeled with elements, called colors, taken from a fixed finite alphabet. We study the problem of determining whether there is an infinite path where either (i) all colors occur with the same asymptotic frequency, or (ii) there is a constant which ..."
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Cited by 2 (2 self)
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Abstract. We consider finite graphs whose edges are labeled with elements, called colors, taken from a fixed finite alphabet. We study the problem of determining whether there is an infinite path where either (i) all colors occur with the same asymptotic frequency, or (ii) there is a constant which
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 679 (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
Balance Games on Colored Graphs
"... Abstract. We consider games played on finite colored graphs for an infinite number of rounds, whose goal is to visit all colors with the same asymptotic frequency. Such games may represent scheduling problems with special fairness constraints. We show that the main corresponding decision problems ar ..."
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are CoNPcomplete. Recently, the following two problems on colored graphs have been addressed and solved [BFMM09]. Consider a directed graph G whose edges are labeled with tags, called colors, belonging to a fixed finite alphabet. The first problem asks whether there exists in G an infinite path ρ where
SemiBalanced Colorings of Graphs
"... Randomness often implies uniformity, but usually there exists a much more uniform distribution than a random distribution. An interesting question is how we can construct a strongly uniform distribution for a given structure. If we have n points on a line, it is easy to color points into red and bl ..."
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color of points from red to bule one by one such that each intermediate sequence is almost “uniform”. It is an interesting question how we can generalize this fact to a more general structure, namely, a graph. Given a graph G = (V,E), a 2coloring of G is a mapping π from V to {red, blue} such that π
On balanced coloring games in random graphs
 Electronic Notes in Discrete Mathematics, 38(0):425 – 430, 2011. Proceedings of the Sixth European Conference on Combinatorics, Graph Theory and Applications (EuroComb
, 2011
"... Abstract. Consider the balanced Ramsey game, in which a player has r colors and where in each step r random edges of an initially empty graph on n vertices are presented. The player has to immediately assign a different color to each edge and her goal is to avoid creating a monochromatic copy of som ..."
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Cited by 1 (1 self)
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Abstract. Consider the balanced Ramsey game, in which a player has r colors and where in each step r random edges of an initially empty graph on n vertices are presented. The player has to immediately assign a different color to each edge and her goal is to avoid creating a monochromatic copy
Paths and cycles in colored graphs
 Australasian J. Combin
"... Let G be an (edge)colored graph. A path (cycle) is called monochromatic if all of its edges have the same color, and is called heterochromatic if all of its edges have different colors. In this paper, some sufficient conditions for the existence of (long) monochromatic paths and cycles, and those f ..."
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Cited by 23 (9 self)
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Let G be an (edge)colored graph. A path (cycle) is called monochromatic if all of its edges have the same color, and is called heterochromatic if all of its edges have different colors. In this paper, some sufficient conditions for the existence of (long) monochromatic paths and cycles, and those
PathFinder: A Negotiationbased Performancedriven Router for FPGAs”, FPGA
, 1995
"... Routing FPGAs is a challenging problem because of the relative scarcity of routing resources, both wires and connection points. This can lead either to slow implementations caused by long wiring paths that avoid congestion or a failure to route all signals. This paper presents PathFinder, a router t ..."
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Cited by 204 (12 self)
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that balances the goals of performance and routability. PathFinder uses an iterative algorithm that converges to a solution in which all signals are routed while achieving close to the optimal performance allowed by the placement. Routability is achieved by forcing signals to negotiate for a resource
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
Balanced coloring of bipartite graphs
, 2009
"... Given a bipartite graph G(U ∪ V, E) with n vertices on each side, an independent set I ∈ G such that U ⋂ I  = V ⋂ I  is called a balanced bipartite independent set. A balanced coloring of G is a coloring of the vertices of G such that each color class induces a balanced bipartite independent se ..."
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Cited by 1 (0 self)
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Given a bipartite graph G(U ∪ V, E) with n vertices on each side, an independent set I ∈ G such that U ⋂ I  = V ⋂ I  is called a balanced bipartite independent set. A balanced coloring of G is a coloring of the vertices of G such that each color class induces a balanced bipartite independent
Results 1  10
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354,705