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Coloration of K−7minor free graphs
, 2014
"... Hadwiger’s conjecture says that every Ktminor free graph is (t − 1)colorable. This problem has been proved for t ≤ 6 but remains open for t ≥ 7. K7minor free graphs have been proved to be 8colorable (Albar & Gonçalves, 2013). We prove here that K−7minor free graphs are 7colorable, where K ..."
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Hadwiger’s conjecture says that every Ktminor free graph is (t − 1)colorable. This problem has been proved for t ≤ 6 but remains open for t ≥ 7. K7minor free graphs have been proved to be 8colorable (Albar & Gonçalves, 2013). We prove here that K−7minor free graphs are 7colorable, where K
Decomposition, approximation, and coloring of oddminorfree graphs
"... We prove two structural decomposition theorems about graphs excluding a fixed odd minor H, and show how these theorems can be used to obtain approximation algorithms for several algorithmic problems in such graphs. Our decomposition results provide new structural insights into oddHminorfree graph ..."
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Cited by 5 (2 self)
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of the wellstudied Hminorfree graph families and includes, for example, all bipartite graphs plus a bounded number of apices. OddHminorfree graphs are particularly interesting from a structural graph theory perspective because they break away from the sparsity of Hminorfree graphs, permitting a quadratic
Flows in onecrossingminorfree graphs
 In ISAAC (1
, 2010
"... Abstract. We study the maximum flow problem in directed Hminorfree graphs where H can be drawn in the plane with one crossing. If a structural decomposition of the graph as a cliquesum of planar graphs and graphs of constant complexity is given, we show that a maximum flow can be computed in O(n ..."
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(n logn) time. In particular, maximum flows in directed K3,3minorfree graphs and directed K5minorfree graphs can be computed in O(n logn) time without additional assumptions. 1
Toughness of Ka,tminorfree graphs
"... S The toughness of a noncomplete graph G is the minimum value of ω(G−S) among all separating vertex sets S ⊂ V (G), where ω(G − S) � 2 is the number of components of G − S. It is wellknown that every 3connected planar graph has toughness greater than 1/2. Related to this property, every 3conn ..."
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connected planar graph has many good substructures, such as a spanning tree with maximum degree three, a 2walk, etc. Realizing that 3connected planar graphs are essentially the same as 3connected K3,3minorfree graphs, we consider a generalization to aconnected Ka,tminorfree graphs, where 3 � a � t
A characterization of K2,4minorfree graphs
, 2014
"... We provide a complete structural characterization of K2,4minorfree graphs. The 3connected K2,4minorfree graphs consist of nine small graphs on at most eight vertices, together with a family of planar graphs that contains K4 and, for each n ≥ 5, 2n − 8 nonisomorphic graphs of order n. To describ ..."
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We provide a complete structural characterization of K2,4minorfree graphs. The 3connected K2,4minorfree graphs consist of nine small graphs on at most eight vertices, together with a family of planar graphs that contains K4 and, for each n ≥ 5, 2n − 8 nonisomorphic graphs of order n
Dynamic Programming for Hminorfree Graphs?
"... Abstract. We provide a framework for the design and analysis of dynamic programming algorithms for Hminorfree graphs with branchwidth at most k. Our technique applies to a wide family of problems where standard (deterministic) dynamic programming runs in 2O(k·log k) · nO(1) steps, with n being t ..."
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Abstract. We provide a framework for the design and analysis of dynamic programming algorithms for Hminorfree graphs with branchwidth at most k. Our technique applies to a wide family of problems where standard (deterministic) dynamic programming runs in 2O(k·log k) · nO(1) steps, with n being
Precoloring extension for K4minorfree graphs
, 2007
"... Let G = (V, E) be a graph where every vertex v ∈ V is assigned a list of available colors L(v). We say that G is list colorable for a given list assignment if we can color every vertex using its list such that adjacent vertices get different colors. If L(v) = {1,..., k} for all v ∈ V then a corresp ..."
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corresponding list coloring is nothing other than an ordinary kcoloring of G. Assume that W ⊆ V is a subset of V such that G[W] is bipartite and each component of G[W] is precolored with two colors. The minimum distance between the components of G[W] is denoted by d(W). We will show that if G is K4minorfree
Stronglybounded sparse decompositions of minor free graphs
 In Proceedings of the Nineteenth Annual ACM Symposium on Parallelism in Algorithms and Architectures (SPAA’07
, 2006
"... As networks grow large and complex, a key approach in managing information and constructing algorithms is to decompose the network into localitypreserving clusters. Then, information and/or management can be divided between the clusters, such that every node is responsible only for clusters for whi ..."
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Cited by 1 (0 self)
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in which the short path between nodes may leave the common cluster and a strong diameter, in which each cluster has a small diameter when considered as an induced subgraph. In this work we present sparse covers and sparse partitions with a bounded strong diameter for the family of minorfree graphs
BOUNDS OF SPECTRAL RADII OF K2,3MINOR FREE GRAPHS ∗
"... Abstract. Let A(G) be the adjacency matrix of a graph G. The largest eigenvalue of A(G) is called spectral radius of G. In this paper, an upper bound of spectral radii of K2,3minor free graphs with order n is shown to be 3 2 + n − 7. In order to prove this upper bound, a structural 4 characterizati ..."
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Abstract. Let A(G) be the adjacency matrix of a graph G. The largest eigenvalue of A(G) is called spectral radius of G. In this paper, an upper bound of spectral radii of K2,3minor free graphs with order n is shown to be 3 2 + n − 7. In order to prove this upper bound, a structural 4
Distance Constrained Labelings of K4minor Free Graphs
, 2006
"... Motivated by previous results on distance constrained labelings and coloring of squares of K4minor free graphs, we show that for every p> = q> = 1, there exists \Delta 0 such that every K4minor free graph G with maximum degree \Delta> = \Delta 0 has an L(p, q)labeling of span at most qb3 ..."
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Motivated by previous results on distance constrained labelings and coloring of squares of K4minor free graphs, we show that for every p> = q> = 1, there exists \Delta 0 such that every K4minor free graph G with maximum degree \Delta> = \Delta 0 has an L(p, q)labeling of span at most qb
Results 1  10
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187,112