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Neighborhood conditions for balanced independent sets in bipartite graphs

1998
*
Discrete Mathematics
*

If,

doi:10.1016/s0012-365x(97)00042-3
fatcat:fln4fmpdsncwtpb25plmc7r76y
*for*every*balanced**independent**set*S of four vertices,*IN*(S)I >n then G is traceable, the circumference is at least 2n -2 and G contains a 2-factor (with only small order exceptional*graphs**for*the ... Let G be a*balanced**bipartite**graph*of order 2n and minimum degree 6(G)>~3. ... Acknowledgements We thank the anonymous referee*for*the excellent report, which helped to improve the presentation and avoid an inaccuracy. ...##
###
Page 2018 of Mathematical Reviews Vol. , Issue 96d
[page]

1996
*
Mathematical Reviews
*

A vertex

*in*a*graph*is said to be split provided its*neighborhood*can be partitioned into a clique and an*independent**set*. ...*For**bipartite**graphs*this theorem is ineffective, but (as pointed out by the author) the*balanced**independence*number can be used instead; the*balanced**independence*number is the maximum size of an*independent*...##
###
The common minimal common neighborhood dominating signed graphs

2013
*
Transactions on Combinatorics
*

*In*this paper, we define the common minimal common neighborhooddominating signed

*graph*(or common minimal $CN$-dominating signedgraph) of a given signed

*graph*and offer a structuralcharacterization of ... sequel, we also obtained switching equivalencecharacterization: $overline{Sigma} sim CMCN(Sigma)$, where$overline{Sigma}$ and $CMCN(Sigma)$ are complementary signedgraph and common minimal $CN$-signed

*graph*... Premnath Reddy, Chairman, Acharya Institutes,

*for*his constant support and encouragement

*for*research and development. ...

##
###
ON LOCALLY-BALANCED 2-PARTITIONS OF BIPARTITE GRAPHS

2020
*
Proceedings of the YSU A: Physical and Mathematical Sciences
*

*In*this paper we prove that the problem of deciding, if a given

*graph*has a locally-

*balanced*$2$-partition with an open

*neighborhood*is $NP$-complete even

*for*$(3,8)$-biregular

*bipartite*

*graphs*. ... A $2$-partition $f$ of a

*graph*$G$ is a \emph{locally-

*balanced*with an open

*neighborhood*}, if

*for*every $v\

*in*V(G)$, $\left\vert \vert \{u\

*in*N_{G}(v)\colon\,f(u)=0\}\vert - \vert \{u\

*in*N_{G}(v)\colon ...

*In*this paper we study locally-

*balanced*2-partitions with an open

*neighborhood*of

*bipartite*

*graphs*. ...

##
###
Multi-dimensional separable critically sampled wavelet filterbanks on arbitrary graphs

2012
*
2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
*

*In*our previous work, we observed an "aliasing" phenomenon

*for*functions defined on

*bipartite*

*graphs*which is analogous to aliasing occurring

*in*the downsampling of regular 1-dimensional signals. ... We exploited these concepts to design critically sampled two-channel wavelet filterbanks

*for*any

*bipartite*

*graph*. ...

*In*[8] , we state necessary and sufficient

*conditions*

*for*a two-channel

*graph*filter-bank on

*bipartite*

*graphs*to provide aliasing-cancellation, perfect reconstruction and orthogonal

*set*of basis (orthogonality ...

##
###
Author index to volume 181 (1998)

1998
*
Discrete Mathematics
*

Ordaz,

doi:10.1016/s0012-365x(97)82062-6
fatcat:sqdp43rjovam5az5gxnwxknhxq
*Neighborhood**conditions**for**balanced**independent**sets**in**bipartite**graphs*(1 3 B6na, M., Permutations with one or two 132-subsequences (Note) (1 3 Bogart, K.P. and G. ... Zhang, Direct constructions*for*certain types of HMOLS (1-3 Alon, N. and E. Halperin,*Bipartite*subgraphs of integer weighted*graphs*(1-3 Amar, D., S. Brandt, D. Brito and O. ...##
###
LOCALLY-BALANCED $k$-PARTITIONS OF GRAPHS

2021
*
Proceedings of the YSU A: Physical and Mathematical Sciences
*

A $k$-partition ($k\geq 2$) $f$ of a

doi:10.46991/pysu:a/2021.55.2.096
fatcat:wq5x6ubdyfdpleavndqjiuenje
*graph*$G$ is a locally-*balanced*with an open*neighborhood*, if*for*every $v\*in*V(G)$ and any $0\leq i<j\leq k-1$ $$\left\vert \vert \{u\*in*N_{G}(v)\colon\,f(u)=i\}\vert ... - \vert \{u\*in*N_{G}(v)\colon\,f(u)=j\}\vert \right\vert\leq 1.$$ A $k$-partition ($k\geq 2$) $f^{\prime}$ of a*graph*$G$ is a locally-*balanced*with a closed*neighborhood*, if*for*every $v\*in*V(G)$ and ...*For*the proof, we are going to construct a*bipartite**graph*G n that satisfies the specified*conditions*. ...##
###
Page 2776 of Mathematical Reviews Vol. , Issue 97E
[page]

1997
*
Mathematical Reviews
*

Summary: “Suppose that G is a

*bipartite**graph*with*bipartition*(X,Y). If |X| =|Y|, then G is called*balanced*. An*independent**set*J of G is equalized if ||J. 1 X|—|JN Y|| <1. ... ; Nanjing); Zhang, Xuerong*Neighborhood*unions and Hamilton cycles*in**bipartite**graphs*. ...##
###
Page 4775 of Mathematical Reviews Vol. , Issue 98H
[page]

1998
*
Mathematical Reviews
*

*conditions*

*for*

*balanced*

*independent*

*sets*

*in*

*bipartite*

*graphs*. ... ) Finding

*independent*

*sets*

*in*K4-free 4-regular connected

*graphs*. ...

##
###
Neighborhood unions and regularity in graphs

2001
*
Theoretical Computer Science
*

One way to generalize the concept of degree

doi:10.1016/s0304-3975(00)00246-2
fatcat:anw2upbwgzef7kprzbvgehalbu
*in*a*graph*is to consider the*neighborhood*N (S) of an*independent**set*S instead of a simple vertex. ...*for*every t6 (resp.*for*every t6s), strongly ut-regular (resp. strongly ut6s-regular) if |N (S1)| = |N (S2)|*for*every pair S1; S2 of*independent**sets*of G (resp. every pair of*independent**sets*of order ... Every connected*bipartite*totally u t -regular*graph*is a*balanced*complete*bipartite**graph*. Proof. ...##
###
Topological bounds for graph representations over any field
[article]

2019
*
arXiv
*
pre-print

The notion of

arXiv:1909.06823v2
fatcat:2evxqydhdvga5e6z3en6amwxee
*independent*representation over a matroid is introduced and used*in*a general theorem having these results as corollaries. Related complexity results are also discussed. ... We also improve the topological bound he obtained*for*the minrank parameter over R– an important*graph*invariant from coding theory – and show that this bound is actually valid*for*all fields as well. ... They are also grateful to Ishay Haviv*for*many helpful comments and especially*for*sharing with them the characterization of the minrank given by Lemma 5: it contributed to improve the paper. ...##
###
Page 4714 of Mathematical Reviews Vol. , Issue 97H
[page]

1997
*
Mathematical Reviews
*

B 50 (1990), no. 2, 254-264; MR 92c:05087], we show that if,

*in*a*balanced**bipartite**graph*G of minimum degree 6, the maximum cardinality apip of a*balanced**independent*subset satisfies api, < 25 — 4, ... Summary: “A necessary and sufficient*condition**for*a special mixed*graph*(whose undirected edge*set*is a spanning tree) to be an Eulerian*graph*is given. ...##
###
Greed is Good: Optimistic Algorithms for Bipartite-Graph Partial Coloring on Multicore Architectures
[article]

2017
*
arXiv
*
pre-print

*In*this work, we propose parallel algorithms

*for*

*bipartite*-

*graph*partial coloring on shared-memory architectures. ... Finally, we propose two costless

*balancing*heuristics

*for*BGPC that can reduce the skewness and imbalance on the cardinality of color

*sets*(almost)

*for*free. ... INTRODUCTION A coloring on a

*graph*G = (V, E) explicitly partitions the vertices

*in*V into a number of disjoint subsets such that two vertices u, v ∈ V that are

*in*the same color

*set*are

*independent*from ...

##
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Extremal bipartite independence number and balanced coloring
[article]

2022
*
arXiv
*
pre-print

Firstly, we show that every sufficiently large

arXiv:2107.02506v2
fatcat:g5zwnkhucbeyhkiz4u4mskzliy
*bipartite**graph*with average degree Δ and with n vertices on each side has a*balanced**independent**set*containing (1-ϵ) logΔ/Δ n vertices from each side*for*... Secondly, we prove that the vertex*set*of every sufficiently large*balanced**bipartite**graph*with maximum degree at most Δ can be partitioned into (1+ϵ)Δ/logΔ*balanced**independent**sets*. ... Acknowledgements We are thankful to Rutger Campbell and Sang-il Oum*for*helping us to improve the writing of this paper. ...##
###
The Complexity of Determining Existence a Hamiltonian Cycle is O(n^3)
[article]

2007
*
arXiv
*
pre-print

The Hamiltonian cycle problem

arXiv:0706.2725v1
fatcat:lkll5jca6reinpckzvtkkssz44
*in*digraph is mapped into a matching cover*bipartite**graph*. Based on this mapping, it is proved that determining existence a Hamiltonian cycle*in**graph*is O(n^3). ... A cycle L is a*set*of arcs (a 1 , a 2 , . . . , a q )*in*a digraph D, which obeys two*conditions*: c1. ... Hopcroft and Karp shows that constructs a perfect matching of*bipartite**in*O((m + n) (n)) [6] . The matching of*bipartite*has a relation with*neighborhood*of X. ...
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