Showing papers in "Electronic Notes in Discrete Mathematics in 2011"

TL;DR: This is the first time that a sublogarithmic broadcast time is proven for a natural setting and this is theFirst time that avoiding doublecontacts reduces the run-time to a smaller order of magnitude.

TL;DR: A reformulation and a Branch-and-price algorithm for the Vehicle Routing Problem with Cross-Docking (VRPCD) is proposed and computational results indicate that the reformulation provides bounds much stronger than network flow bounds from previous studies.

TL;DR: Achlioptas, DʼSouza and Spencer as mentioned in this paper proved discontinuous phase transitions for a class of ER-like processes in which in every step we connect two vertices, one chosen randomly from all vertices and one chosen from a restricted set of vertices.

TL;DR: It is shown that deciding if h n ( G ) ⩽ k is an NP-complete problem, even if G is bipartite, and it is proved that hn ( G) can be computed in polynomial time for cactus and P 4 -sparse graphs.

TL;DR: It is proved that it is hard to approximate within a factor of O ( n 1 3 − ϵ ) , for any ϵ > 0, unless NP=ZPP, and it is APX -complete when restricted to bipartite graphs of degree at most 3.

TL;DR: It is proved that for a graph G on n vertices that is chordal or chordal bipartite, if G is k-colourable, then the reconfiguration graph of its l-colourings is connected and has diameter O(n2), and the bound is asymptotically tight up to a constant factor.

TL;DR: It is proved that every graph with maximum degree Δ at least 4 and maximum average degree less that 7 3 admits a 2-distance ( Δ + 1 ) -coloring.

TL;DR: This work addresses uncertainty in the ore-grade of an open-pit mining problem involving extraction and processing decisions under capacity constraints, and applies and compares the risk-hedging performance of three approaches for optimization under uncertainty: Value-at-Risk, Conditional Value- at-R risk and a proposed robust optimization approach.

TL;DR: The rainbow connection of a graph is (at most) reciprocal to its minimum degree, improving the previously best known bound of 20 n / δ from Krivelevich and Yuster, 2010 and showing that every bridge-less chordal graph G has this bound.

TL;DR: The purpose is to minimize the total size of set (multi)systems F, such that for any at most k members of F a system of representatives can be chosen in which each element represents at most t selected members.

TL;DR: It is shown that the constructions of extremal Ktsub2,2-free and K3,3-free graphs cannot be generalized to a similar construction of Ks,s- free graphs for s ⩾ 4 .

TL;DR: Jaegerʼs alternate formulation of Petersen coloring in terms of special five-edge colorings is developed, and a weaker conjecture is suggested, and new techniques to solve it are provided.

TL;DR: In this paper, it was shown that octants are cover-decomposable, i.e., any 12-fold covering of any subset of the space with a finite number of translates of a given octant can be decomposed into two coverings.

TL;DR: It is proved that every 3-uniform n-vertex (n even) hypergraph H with minimum vertex degree δ 1 ( H ) ⩾ ( 7 16 + o ( 1 ) ) ( n 2 ) contains a loose Hamilton cycle.

TL;DR: A new combinatorial abstraction for the graphs of polyhedra is introduced, with each collection of properties taken providing a variant for studying the diameters of polyhedral graphs, and one particular variant has superlinear asymptotic diameter.

TL;DR: It is proved that every graph G with Δ ( G) ⩾ 5 and mad ( G ) 13 5 can be avd-colored with Δ( G ) + 1 colors.

TL;DR: It is shown that the coloring problem for B k -VPG graphs, for k ⩾ 0 , is NP-complete and given a 2-approximation algorithm for coloring B 0 -V PG graphs.

TL;DR: It is proved that it is NP-complete to decide for a given bipartite graph G and a given integer k, whether the P 3 -Caratheodory number of G is at least k.

TL;DR: New reoptimization techniques are developed and applied to the Steiner Tree Problem, which significantly improves the previous results and applies to a variety of re Optimization problems.

TL;DR: In this paper, the authors proposed a randomized rumor spreading protocol with an asymptotically optimal running time of ( 1 + o( 1 ) ) log 2 n. The protocol can spread a rumor from one node to all other nodes in O(nf(n) calls, where f ( n ) = ω ( 1 ) can be arbitrary.

TL;DR: It is shown that for r > 2 the authors can determine f ( r, k ) exactly, and its value is rk, and it is proved to be true only for k ⩽ 4 , so the value of f ( 2, 5 ) is not known.

TL;DR: For a graph G, the largest integer h, such that there are two disjoint homometric sets of order h in G, is denoted by h (G ) as mentioned in this paper.

TL;DR: This work begins the pursuit of a characterization theorem analogous to the one above by Grotschel, Lovasz and Schrijver, replacing the theta body of G by N + ( G ) and searching for the combinatorial counterpart to replace the class of perfect graphs.

TL;DR: It is shown that in any edge-colouring of the complete graph by three colours, it is possible to cover all the vertices by three disjoint monochromatic paths, which solves a particular case of a conjecture of Gyarfas.

TL;DR: It is proved that the universal tournament conjecture holds for all sufficiently large n and that any tournament on 2 n − 2 vertices contains any directed tree on n vertices.

TL;DR: The function rck(G) was introduced by Chartrand et al. in 2008, and has since attracted considerable interest, and is considered for complete bipartite and multipartite graphs, highly connected graphs, and random graphs.

TL;DR: The results imply the existence of a linear algorithm that, given an outerplanar graph, outputs its matroid pathwidth, and a decomposition lemma for proving lower bounds on matroidPathwidth and a relation between matroidpathwidth and linear-width are combined.

TL;DR: A 2D bin packing problem, in which the items to be packed are squares and the bins are unit squares, and it is shown that this game converges to a Nash equilibrium, independently of the packing algorithm used.

TL;DR: A 3/2-approximation algorithm for 2-CRP, a special case of CRP restricted to paths in which the number of vertices of each color is at most 2, is investigated.

TL;DR: It is shown that this concept can naturally be represented in the context of hypergraph theory, and that decisiveness can be decided for simple games in quasi-polynomial time, and for weighted games in polynomial time.