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Erratum For 'A Bound on the Number of Edges in Graphs Without an Even Cycle'

2017 Combinatorics, probability & computing  
For a new discussion on the limit of the method used in this paper see the revised arXiv version of the paper.  ...  Due to a calculation error, the constant in the main theorem is not $80 \sqrt{k\log k}$ but $80\sqrt{k} \log k$ . The error was discovered by Xizhi Liu.  ...  For a new discussion on the limit of the method used in this paper see the revised arXiv version of the paper. 2010 Mathematics subject classification: Primary 05C35 Secondary 05D99, 05C38 Error.  ... 
doi:10.1017/s0963548317000396 fatcat:fv3ad2ryrvbndlkjhzyuy2tid4

Page 8940 of Mathematical Reviews Vol. , Issue 2003m [page]

2003 Mathematical Reviews  
Summary: “In this paper we show that the chromatic number of intersection graphs of congruent geometric figures obtained by translations of a fixed figure in the plane is bounded by the clique number.  ...  G. (1-ILCC; Chicago, IL) Bounds on the chromatic number of intersection graphs of sets in the plane. (English summary) Discrete Math. 262 (2003), no. 1-3, 221-227.  ... 

Page 2470 of Mathematical Reviews Vol. , Issue 89E [page]

1989 Mathematical Reviews  
Let f(k,r) be the minimum number of cycles possible in a k- connected finite simple graph with cycle rank r.  ...  On the other hand, an infinite family of graphs in G*(n, 2n — 2) which contain no cycle longer than c\/n is presented.  ... 

Page 800 of Mathematical Reviews Vol. 58, Issue 2 [page]

1979 Mathematical Reviews  
Kel’mans, A. K. 58 #5372 Erratum: “A certain polynomial of a graph and graphs with an extremal number of trees” (J. Combin. Theory Ser. B 16 (1974), no. 3, 197-214) by the author and V. M. Chelnokov.  ...  For a digraph D without loops or multiple arcs, 1((D) denotes the set of Hamiltonian cycles of D.  ... 

Page 42 of Mathematical Reviews Vol. , Issue 83a [page]

1983 Mathematical Reviews  
Author’s summary: “An m-grapk is a graph, without loops, but with multiple edges of any multiplicity less than or equal to m. An exact m-graph is an m-graph with at least one edge of multiplicity m.  ...  For infinite graphs, the authors observe that the conclusion still holds if the lengths of the shortest odd cycles in each component are bounded; in particular, any graph with only finitely many components  ... 

Page 6644 of Mathematical Reviews Vol. , Issue 90K [page]

1990 Mathematical Reviews  
most two) has an even number of occurrences of each color (such paths are called even paths) if and only if it is a cycle.  ...  The resulting parallel preprocessing algorithm runs in logarithmic time using an optimal number of processors on an EREW PRAM.  ... 

Page 3457 of Mathematical Reviews Vol. , Issue 87g [page]

1987 Mathematical Reviews  
The main result of this paper is the following: Hg is balanced if and only if G is triangulated and every cycle in G whose length is of the form 4m + 2 has an even chord.  ...  In the present paper, the author describes a method for obtaining a new (and possibly small) k-clique from old ones, improving the previous upper bounds on m(k) for several values of k.  ... 

Multi-Pass Graph Streaming Lower Bounds for Cycle Counting, MAX-CUT, Matching Size, and Other Problems [article]

Sepehr Assadi, Gillat Kol, Raghuvansh R. Saxena, Huacheng Yu
2021 arXiv   pre-print
Consider the following gap cycle counting problem in the streaming model: The edges of a 2-regular n-vertex graph G are arriving one-by-one in a stream and we are promised that G is a disjoint union of  ...  For all these problems, prior work left open the possibility of even an O(logn) space algorithm in only two passes.  ...  Define X := n/k i=1 X i which lower bounds the number of odd cycles in H.  ... 
arXiv:2009.03038v2 fatcat:e7d3uwx5unhq3bzsihmnxzykeu

Negative (and Positive) Circles in Signed Graphs: A Problem Collection [article]

Thomas Zaslavsky
2018 arXiv   pre-print
A signed graph is a graph whose edges are labelled positive or negative. The sign of a circle (cycle, circuit) is the product of the signs of its edges.  ...  Most of the essential properties of a signed graph depend on the signs of its circles. Here I describe several questions regarding negative circles and their cousins the positive circles.  ...  In [HK] the same authors and King study the property of strong circle decomposability of a graph Γ: every subdivision of Γ with an even number of edges decomposes into even circles.  ... 
arXiv:1701.07963v2 fatcat:coipmzw7djeq7lf46caynjeis4

Unrooted non-binary tree-based phylogenetic networks [article]

Mareike Fischer and Michelle Galla and Lina Herbst and Yangjing Long and Kristina Wicke
2020 arXiv   pre-print
Typically, such networks have been analyzed based on their 'level', i.e. based on the complexity of their 2-edge-connected components.  ...  However, recently the question of how 'treelike' a phylogenetic network is has become the center of attention in various studies.  ...  Moreover, the second author thanks the University of Greifswald for the Bogislaw-Studentship and the fifth author thanks the German Academic Scholarship Foundation for a studentship.  ... 
arXiv:1810.06853v4 fatcat:gnq3hq7xuzhw7jverymch4ap3u

Enumeration of edge-critical underlying absolute planar cliques for signed graphs

Julien Bensmail, Soumen Nandi, Mithun Roy, Sagnik Sen
2020 The Australasian Journal of Combinatorics  
A closed walk of a signed graph is positive (negative) if it has an even (odd) number of negative edges, taking repeated edges into account.  ...  A simple signed graph (G, Σ) is a simple graph G having two different types of edges, positive edges and negative edges, where Σ denotes the set of negative edges of G.  ...  Acknowledgements We would like to thank the anonymous reviewers for their careful scrutiny of our work and for raising valuable and discerning comments.  ... 
dblp:journals/ajc/BensmailNR020 fatcat:s7djue2gvrfhxaj4lafebvpdau

TS2PACK: A two-level tabu search for the three-dimensional bin packing problem

Teodor Gabriel Crainic, Guido Perboli, Roberto Tadei
2009 European Journal of Operational Research  
We present a two-level tabu search for this problem. The first level aims to reduce the number of bins. The second optimizes the packing of the bins.  ...  Three-dimensional orthogonal bin packing is a problem NP-hard in the strong sense where a set of boxes must be orthogonally packed into the minimum number of three-dimensional bins.  ...  Acknowledgements Partial funding for this project has been provided by the Natural Sciences and Engineering Council of Canada.  ... 
doi:10.1016/j.ejor.2007.06.063 fatcat:octgbu5n2rcwxeuhxj73kvatoe

A list analog of Vizing's Theorem for simple graphs with triangles but no other odd cycles [article]

Jessica McDonald
2015 arXiv   pre-print
This paper has been withdrawn by the author. Peterson and Woodall previously proved that the list-edge-colouring conjecture holds for graphs without odd cycles of length 5 or longer. D.  ...  Woodall, Erratum to "Edge-choosability in line-perfect multigraphs", Discrete Mathematics 260 (2003), 323-326.  ...  (Maffray [6] ) A simple graph G has no odd cycles of length 5 or longer iff every block B of G satisfies one of the following: Acknowledgments I thank Dean Hoffman for his many helpful comments.  ... 
arXiv:1407.0626v2 fatcat:rcjdtqvnrbe2bdhehocclurksm


2013 Discrete Mathematics, Algorithms and Applications (DMAA)  
Recently, Ganesan computed β, an estimate of the exact upper bound for the same, in O(n 2 ) time. Our upper bounds are tighter than f (Γ ) and β, on average and in most of the cases.  ...  An upper bound for sorting permutations with an operation estimates the diameter of the corresponding Cayley graph and an exact upper bound equals the diameter.  ...  If a degenerate tree has an even number of vertices then the center is an edge, otherwise, the center is a vertex. Any path of length diam(T ) passes through the center.  ... 
doi:10.1142/s1793830913920018 fatcat:jcbkcqbzgvhxxoktthj6hu6kzi

Directed Cycles in Bayesian Belief Networks: Probabilistic Semantics and Consistency Checking Complexity [chapter]

Alexander L. Tulupyev, Sergey I. Nikolenko
2005 Lecture Notes in Computer Science  
We propose a simple way of explicating the probabilistic relationships an isolated directed cycle contains, give an algorithm (based on linear programming) of its consistency checking, and establish a  ...  lower bound of the complexity of this checking.  ...  They have a complex structure with three different kinds of edges and allow undirected cycles in the graph.  ... 
doi:10.1007/11579427_22 fatcat:cuik3x6shjg2ba362ceegoibce
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