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271
Planar Packing of DiameterFour Trees
"... We prove that, for every two nnode nonstar trees of diameter at most four, there exists an nnode planar graph containing them as edgedisjoint subgraphs. 1 ..."
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We prove that, for every two nnode nonstar trees of diameter at most four, there exists an nnode planar graph containing them as edgedisjoint subgraphs. 1
Edgedisjoint induced subgraphs with given minimum degree
"... Let h be a given positive integer. For a graph with n vertices and m edges, what is the maximum number of pairwise edgedisjoint induced subgraphs, each having minimum degree at least h? There are examples for which this number is O(m 2 /n 2). We prove that this bound is achievable for all graphs wi ..."
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Let h be a given positive integer. For a graph with n vertices and m edges, what is the maximum number of pairwise edgedisjoint induced subgraphs, each having minimum degree at least h? There are examples for which this number is O(m 2 /n 2). We prove that this bound is achievable for all graphs
Characterizing randomly Pkdecomposable graphs for k ≤ 9
"... A graph G is randomly H–decomposable if every family of edge disjoint subgraphs of G, each subgraph isomorphic to H, can be extended to an H–decomposition of G. Let Pk denote a path of length k. In this paper we characterize randomly Pk–decomposable graphs for k ≤ 9. ..."
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A graph G is randomly H–decomposable if every family of edge disjoint subgraphs of G, each subgraph isomorphic to H, can be extended to an H–decomposition of G. Let Pk denote a path of length k. In this paper we characterize randomly Pk–decomposable graphs for k ≤ 9.
Packing Steiner trees
"... The Steiner packing problem is to find the maximum number of edgedisjoint subgraphs of a given graph G that connect a given set of required points S. This problem is motivated by practical applications in VLSIlayout and broadcasting, as well as theoretical reasons. In this paper, we study this p ..."
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Cited by 108 (5 self)
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The Steiner packing problem is to find the maximum number of edgedisjoint subgraphs of a given graph G that connect a given set of required points S. This problem is motivated by practical applications in VLSIlayout and broadcasting, as well as theoretical reasons. In this paper, we study
Two EdgeDisjoint HopConstrained Paths and Polyhedra
 SIAM J. Discrete Math
, 2002
"... Given a graph G with distinguished nodes s and t, a cost on each edge of G, and a xed integer L 2, the Two edgedisjoint Hopconstrained Paths Problem (THPP for short) is to nd a minimum cost subgraph such that between s and t there exist at least two edgedisjoint paths of length at most L. In thi ..."
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Cited by 11 (1 self)
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Given a graph G with distinguished nodes s and t, a cost on each edge of G, and a xed integer L 2, the Two edgedisjoint Hopconstrained Paths Problem (THPP for short) is to nd a minimum cost subgraph such that between s and t there exist at least two edgedisjoint paths of length at most L
Symmetric Class 0 subgraphs of complete graphs
, 2011
"... In graph pebbling, a connected graph is called Class 0 if it has a pebbling number equal to its number of vertices. This paper addresses the question of when it is possible to edgepartition a complete graph into k complementary Class 0 subgraphs. We define the notion of kClass 0 graphs: a graph G ..."
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is kClass 0 if it contains k edgedisjoint subgraphs, where each subgraph is Class 0. We next present a family of kClass 0 graphs for k = 2, showing that for n ≥ 9, Kn is 2Class 0. We finally provide a probabilistic argument to prove that ∀k ∈ N, ∃n ∈ N such that Kn can be edgepartitioned into k
Simultaneous wellbalanced orientations of graphs
, 2008
"... NashWilliams’ wellbalanced orientation theorem [11] is extended for orienting several graphs simultaneously. We prove that if G1,..., Gk are pairwise edgedisjoint subgraphs of a graph G, then G has a wellbalanced orientation ~G such that the inherited orientations ~Gi of Gi are wellbalanced for ..."
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Cited by 8 (3 self)
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NashWilliams’ wellbalanced orientation theorem [11] is extended for orienting several graphs simultaneously. We prove that if G1,..., Gk are pairwise edgedisjoint subgraphs of a graph G, then G has a wellbalanced orientation ~G such that the inherited orientations ~Gi of Gi are well
Induced ∆Decomposition of Graphs
, 2012
"... Abstract A decomposition of a graph is a collection of edgedisjoint subgraphs , , … of such that every edge of belongs to exactly one . A decomposition = { , , … … , } is called a ∆decomposition if the maximum degree of is for each . A ∆decomposition = { , , … … , } of a graph G is called an ind ..."
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Abstract A decomposition of a graph is a collection of edgedisjoint subgraphs , , … of such that every edge of belongs to exactly one . A decomposition = { , , … … , } is called a ∆decomposition if the maximum degree of is for each . A ∆decomposition = { , , … … , } of a graph G is called
The Countable Character of Uncountable Graphs
, 2004
"... We show that a graph can always be decomposed into edgedisjoint subgraphs of countable cardinality in which the edgeconnectivities and edgeseparations of the original graph are preserved up to countable cardinals. We also show that the vertex set of any graph can be endowed with a wellordering w ..."
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We show that a graph can always be decomposed into edgedisjoint subgraphs of countable cardinality in which the edgeconnectivities and edgeseparations of the original graph are preserved up to countable cardinals. We also show that the vertex set of any graph can be endowed with a well
The edgedisjoint paths problem is NPcomplete for series–parallel graphs,
, 1998
"... Abstract Many combinatorial problems are NPcomplete for general graphs. However, when restricted to seriesparallel graphs or partial ktrees, many of these problems can be solved in polynomial time, mostly in linear time. On the other hand, very few problems are known to be NPcomplete for series ..."
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Cited by 16 (1 self)
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complete for seriesparallel graphs or partial ktrees. These include the subgraph isomorphism problem and the bandwidth problem. However, these problems are NPcomplete even for trees. In this paper, we show that the edgedisjoint paths problem is NPcomplete for seriesparallel graphs and for partial 2trees
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