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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. ...

##
###
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]

2021
*
arXiv
*
pre-print

Consider

arXiv:2009.03038v2
fatcat:e7d3uwx5unhq3bzsihmnxzykeu
*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. ...##
###
Negative (and Positive) Circles in Signed Graphs: A Problem Collection
[article]

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. ...

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

2020
*
arXiv
*
pre-print

Typically, such networks have been analyzed based

arXiv:1810.06853v4
fatcat:gnq3hq7xuzhw7jverymch4ap3u
*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. ...##
###
Enumeration of edge-critical underlying absolute planar cliques for signed graphs

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. ...

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

2009
*
European Journal of Operational Research
*

We present

doi:10.1016/j.ejor.2007.06.063
fatcat:octgbu5n2rcwxeuhxj73kvatoe
*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. ...##
###
A list analog of Vizing's Theorem for simple graphs with triangles but no other odd cycles
[article]

2015
*
arXiv
*
pre-print

This paper has been withdrawn by

arXiv:1407.0626v2
fatcat:rcjdtqvnrbe2bdhehocclurksm
*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. ...##
###
ERRATUM: "UPPER BOUNDS FOR SORTING PERMUTATIONS WITH A TRANSPOSITION TREE"

2013
*
Discrete Mathematics, Algorithms and Applications (DMAA)
*

Recently, Ganesan computed β,

doi:10.1142/s1793830913920018
fatcat:jcbkcqbzgvhxxoktthj6hu6kzi
*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. ...##
###
Directed Cycles in Bayesian Belief Networks: Probabilistic Semantics and Consistency Checking Complexity
[chapter]

2005
*
Lecture Notes in Computer Science
*

We propose

doi:10.1007/11579427_22
fatcat:cuik3x6shjg2ba362ceegoibce
*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*. ...
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