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An Asymptotic Approximation Scheme for Multigraph Edge
"... Abstract The edge coloring problem asks for assigning colors from a minimum number of colors to edges of a graph such that no two edges with the same color are incident to the same node. We give polynomial time algorithms for approximate edge coloring of multigraphs, i.e., parallel edges are allowed ..."
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Abstract The edge coloring problem asks for assigning colors from a minimum number of colors to edges of a graph such that no two edges with the same color are incident to the same node. We give polynomial time algorithms for approximate edge coloring of multigraphs, i.e., parallel edges
Approximating Maximum Edge Coloring in Multigraphs
 In APPROX, volume 2462 of LNCS
, 2002
"... We study the complexity of the following problem that we call Max edge tcoloring: given a multigraph G and a parameter t, color as many edges as possible using t colors, such that no two adjacent edges are colored with the same color. (Equivalently, find the largest edge induced subgraph of G that ..."
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We study the complexity of the following problem that we call Max edge tcoloring: given a multigraph G and a parameter t, color as many edges as possible using t colors, such that no two adjacent edges are colored with the same color. (Equivalently, find the largest edge induced subgraph of G
Approximating the chromatic index of multigraphs
"... It is well known that if G is a multigraph then χ ′(G) ≥ χ ′∗(G): = max{∆(G), Γ(G)}, where χ ′(G) is the chromatic index of G, χ ′∗(G) is the fractional chromatic index of G, ∆(G) is the maximum degree of G, and Γ(G) = max{2E(G[U])/(U  − 1) : U ⊆ V (G), U  ≥ 3, U  is odd}. The conjecture ..."
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this conjecture for multigraphs G with χ ′(G)> ⌊(11∆(G) + 8)/10⌋; and Scheide recently improved this bound to χ ′(G)> ⌊(15∆(G) + 12)/14⌋. We prove this conjecture for multigraphs G with χ ′(G)> ⌊∆(G) + √ ∆(G)/2⌋, improving the above mentioned results. Our proof yields an algorithm for edgecoloring any
Min sum edge coloring in multigraphs via configuration LP
 In Proc. of IPCO’08, LNCS
, 2008
"... We consider the scheduling of biprocessor jobs under sum objective (BPSMS). Given a collection of unitlength jobs where each job requires the use of two processors, find a schedule such that no two jobs involvingthe same processorrun concurrently. The objectiveis to minimize the sum of the completi ..."
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of the completion times of the jobs. Equivalently, we would like to find a sum edge coloring of a given multigraph, i.e. a partition of its edge set into matchings M1,...,Mt minimizing ∑ t i=1 iMi. This problem is APXhard, even in the case of bipartite graphs [M04]. This special case is closely related
On the Ramsey Numbers for Bipartite Multigraphs
, 2003
"... A coloring of a complete bipartite graph is shufflepreserved if it is the case that assigning a color c to edges (u,v) and (u′,v ′) enforces the same color assignment for edges (u,v ′) and (u′,v). (In words, the induced subgraph with respect to color c is complete.) In this paper, we investigate a ..."
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variant of the Ramsey problem for the class of complete bipartite multigraphs. (By a multigraph we mean a graph in which multiple edges, but no loops, are allowed.) Unlike the conventional mcoloring scheme in Ramsey theory which imposes a constraint (i.e., m) on the total number of colors allowed in a
Edge Coloring with Delays
"... Consider the following communication problem, that leads to a new notion of edge coloring. The communication network is represented by a bipartite multigraph, where the nodes on one side are the transmitters and the nodes on the other side are the receivers. The edges correspond to messages, and eve ..."
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Consider the following communication problem, that leads to a new notion of edge coloring. The communication network is represented by a bipartite multigraph, where the nodes on one side are the transmitters and the nodes on the other side are the receivers. The edges correspond to messages
Chromatic Edge Strength of Some Multigraphs
, 2007
"... The edge strength s ′ (G) of a multigraph G is the minimum number of colors in a minimum sum edge coloring of G. We give closed formulas for the edge strength of bipartite multigraphs and multicycles. These are shown to be classes of multigraphs for which the edge strength is always equal to the chr ..."
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The edge strength s ′ (G) of a multigraph G is the minimum number of colors in a minimum sum edge coloring of G. We give closed formulas for the edge strength of bipartite multigraphs and multicycles. These are shown to be classes of multigraphs for which the edge strength is always equal
Results 1  10
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169,899