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Acyclic Edge Coloring of Subcubic Graphs
"... An acyclic edge coloring of a graph is a proper edge coloring such that there are no bichromatic cycles. The acyclic chromatic index of a graph is the minimum number k such that there is an acyclic edge coloring using k colors and is denoted by a ′ (G). From a result of Burnstein it follows that all ..."
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Cited by 9 (0 self)
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that all subcubic graphs are acyclically edge colorable using 5 colors. This result is tight since there are 3regular graphs which require 5 colors. In this paper we prove that any nonregular connected graph of maximum degree 3 is acyclically edge colorable using at most 4 colors. This result is tight
On List EdgeColorings of Subcubic Graphs
 DISCRETE MATH
"... In this paper we study list edgecolorings of graphs with small maximal degree. In particular, we show that simple subcubic graphs are "10/3edgechoosable". The precise meaning of this statement is that no matter how we prescribe arbitrary lists of three colors on edges of a subgraph H of ..."
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of G such that \Delta(H ) 2, and prescribe lists of four colors on E(G)nE(H), the subcubic graph G will have an edgecoloring with the given colors. Several consequences follow from this result.
Linear balanceable and subcubic balanceable graphs
, 2012
"... In [Structural properties and decomposition of linear balanced matrices, Mathematical Programming, 55:129–168, 1992], Conforti and Rao conjectured that every balanced bipartite graph contains an edge that is not the unique chord of a cycle. We prove this conjecture for balanced bipartite graphs tha ..."
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that do not contain a cycle of length 4 (also known as linear balanced bipartite graphs), and for balanced bipartite graphs whose maximum degree is at most 3. We in fact obtain results for more general classes, namely linear balanceable and subcubic balanceable graphs. Additionally, we prove that cubic
Efficient Subcubic Alias Analysis for C
"... Abstract Inclusionbased alias analysis for C can be formulated as a contextfree language (CFL) reachability problem. It is well known that the traditional cubic CFLreachability algorithm does not scale well in practice. We present a highly scalable and efficient CFLreachabilitybased alias anal ..."
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enabling technique in the subcubic CFLreachability algorithm in our alias analysis. We have implemented our subcubic alias analysis and conducted extensive experiments on widelyused C programs from the pointer analysis literature. The results demonstrate that our alias analysis scales extremely well
Median eigenvalues of bipartite subcubic graphs
 Combinatorics, Probability & Computing
"... It is proved that the median eigenvalues of every connected bipartite graph G of maximum degree at most three belong to the interval [−1, 1] with a single exception of the Heawood graph, whose median eigenvalues are ±√2. Moreover, if G is not isomorphic to the Heawood graph, then a positive fraction ..."
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fraction of its median eigenvalues lie in the interval [−1, 1]. This surprising result has been motivated by the problem about HOMOLUMO separation that arises in mathematical chemistry. 2010 Mathematics Subject Classification: 05C50 1
Listcoloring the square of a subcubic graphs
, 2007
"... The square G 2 of a graph G is the graph with the same vertex set as G and with two vertices adjacent if their distance in G is at most 2. Thomassen showed that for a planar graph G with maximum degree ∆(G) = 3 we have χ(G 2) ≤ 7. Kostochka and Woodall conjectured that for every graph, the listch ..."
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chromatic number of G 2 equals the chromatic number of G 2, that is χl(G 2) = χ(G 2) for all G. If true, this conjecture (together with Thomassen’s result) implies that every planar graph G with ∆(G) = 3 satisfies χl(G 2) ≤ 7. We prove that every graph (not necessarily planar) with ∆(G) = 3 other than
Trianglefree subcubic graphs with minimum bipartite density
 J. Combin. Theory Ser. B
"... A graph is subcubic if its maximum degree is at most 3. The bipartite density of a graph G is max{ε(H)/ε(G) : H is a bipartite subgraph of G}, where ε(H) and ε(G) denote the numbers of edges in H and G, respectively. It is an NPhard problem to determine the bipartite density of any given trianglef ..."
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and Locke further conjectured that there are precisely seven trianglefree subcubic graphs with bipartite density 4 5. We prove this conjecture of Bondy and Locke. Our result will be used in a forthcoming paper to solve a problem of Bollobás and Scott related to judicious partitions.
Packing ThreeVertex Paths in a Subcubic Graph
, 2005
"... In our paper we consider the P3packing problem in subcubic graphs of different connectivity, improving earlier results of Kelmans and Mubayi (5). We show that there exists a P3packing of at least ⌈3n/4 ⌉ vertices in any connected subcubic graph of order n> 5 and minimum vertex degree δ ≥ 2, and ..."
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In our paper we consider the P3packing problem in subcubic graphs of different connectivity, improving earlier results of Kelmans and Mubayi (5). We show that there exists a P3packing of at least ⌈3n/4 ⌉ vertices in any connected subcubic graph of order n> 5 and minimum vertex degree δ ≥ 2
Listcolouring squares of sparse subcubic graphs
, 2005
"... The problem of colouring the square of a graph naturally arises in connection with the distance labelings, which have been studied intensively. We consider this problem for sparse subcubic graphs. We show that the choosability χℓ(G2) of the square of a subcubic graph G of maximum average degree d is ..."
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is at most four if d<24/11 and G does not contain a 5cycle, χℓ(G2)isatmostfiveifd<7/3 and it is at most six if d<5/2. Wegner’s conjecture claims that the chromatic number of the square of a subcubic planar graph is at most seven. Let G be a planar subcubic graph of girth g. Our result implies
A Combinatorial Analysis of Subcube Reliability in Hypercubes
"... AbstractIn this brief contribution, we derive an exact expression for (n 1)cube reliability in an ncube using a new probability fault model and M existing random fault model. Approximate results are also obtained for mcube reliability for values of m smaller than n I. We show that the propose ..."
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AbstractIn this brief contribution, we derive an exact expression for (n 1)cube reliability in an ncube using a new probability fault model and M existing random fault model. Approximate results are also obtained for mcube reliability for values of m smaller than n I. We show
Results 1  10
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