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Neighborhood conditions for balanced independent sets in bipartite graphs

Denise Amar, Stephan Brandt, Daniel Brito, Oscar Ordaz
1998 Discrete Mathematics  
If, 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.  ... 
doi:10.1016/s0012-365x(97)00042-3 fatcat:fln4fmpdsncwtpb25plmc7r76y

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

Kavita S Permi, K.R. Rajanna, P.Siva Kota Reddy
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.  ... 
doaj:f701a79d45ac40ed93481aaf2b4f47e7 fatcat:egzjthkn2fbabbiqxacamvh4ke

ON LOCALLY-BALANCED 2-PARTITIONS OF BIPARTITE GRAPHS

Aram H. Gharibyan, Petros A. Petrosyan
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.  ... 
doi:10.46991/pysu:a/2020.54.3.137 fatcat:ncxzn4nzzncstifplt66c6l7se

Multi-dimensional separable critically sampled wavelet filterbanks on arbitrary graphs

Sunil K Narang, Antonio Ortega
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  ... 
doi:10.1109/icassp.2012.6288671 dblp:conf/icassp/NarangO12 fatcat:3hzmyve5hjffte3aai3izdazei

Author index to volume 181 (1998)

1998 Discrete Mathematics  
Ordaz, 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.  ... 
doi:10.1016/s0012-365x(97)82062-6 fatcat:sqdp43rjovam5az5gxnwxknhxq

LOCALLY-BALANCED $k$-PARTITIONS OF GRAPHS

Aram H. Gharibyan, Petros A. Petrosyan
2021 Proceedings of the YSU A: Physical and Mathematical Sciences  
A $k$-partition ($k\geq 2$) $f$ of a 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.  ... 
doi:10.46991/pysu:a/2021.55.2.096 fatcat:wq5x6ubdyfdpleavndqjiuenje

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

O. Favaron, Y. Redouane
2001 Theoretical Computer Science  
One way to generalize the concept of degree 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.  ... 
doi:10.1016/s0304-3975(00)00246-2 fatcat:anw2upbwgzef7kprzbvgehalbu

Topological bounds for graph representations over any field [article]

Meysam Alishahi, Frédéric Meunier
2019 arXiv   pre-print
The notion of 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.  ... 
arXiv:1909.06823v2 fatcat:2evxqydhdvga5e6z3en6amwxee

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]

Mustafa Kemal Taş, Kamer Kaya, Erik Saule
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  ... 
arXiv:1701.02628v1 fatcat:ftnvadp3vrc4defgj7odfh34ja

Extremal bipartite independence number and balanced coloring [article]

Debsoumya Chakraborti
2022 arXiv   pre-print
Firstly, we show that every sufficiently large 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.  ... 
arXiv:2107.02506v2 fatcat:g5zwnkhucbeyhkiz4u4mskzliy

The Complexity of Determining Existence a Hamiltonian Cycle is O(n^3) [article]

Guohun Zhu
2007 arXiv   pre-print
The Hamiltonian cycle problem 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.  ... 
arXiv:0706.2725v1 fatcat:lkll5jca6reinpckzvtkkssz44
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