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1. 2-Proper Partition of a Graph

   **aodong Chen, **yao Guo, **wu Yang in Graphs and Combinatorics

   Article 26 November 2022

2. SDP-based bounds for graph partition via extended ADMM

   We study two NP-complete graph partition problems, k -equipartition problems and graph partition problems with knapsack constraints (GPKC). We...

   Angelika Wiegele, Shudian Zhao in Computational Optimization and Applications

   Article Open access 17 March 2022
   

3. The Strong Spectral Property of Graphs: Graph Operations and Barbell Partitions

   The utility of a matrix satisfying the Strong Spectral Property has been well established particularly in connection with the inverse eigenvalue...

   Sarah Allred, Emelie Curl, ... Prateek K. Vishwakarma in Graphs and Combinatorics

   Article 06 February 2024
   

4. Perfect state transfer, equitable partition and continuous-time quantum walk based search

   In this paper, we consider a continuous-time quantum walk based search algorithm. We discuss equitable partition of the graph and perfect state...

   Yusuke Ide, Akihiro Narimatsu in Quantum Studies: Mathematics and Foundations

   Article 16 February 2024

5. Singleton coalition graph chains

   Davood Bakhshesh, Michael A. Henning, Dinabandhu Pradhan in Computational and Applied Mathematics

   Article 08 February 2024
   

6. Partitioning planar graph of girth 5 into two forests with maximum degree 4

   Given a graph G = ( V, E ), if we can partition the vertex set V into two nonempty subsets V ₁ and V ₂ which satisfy Δ( G [ V ₁ ]) ⩽ d ₁ and Δ( G [ V ₂ ]) ⩽ d ₂ ,...

   Min Chen, André Raspaud, ... Weiqiang Yu in Czechoslovak Mathematical Journal

   Article 30 May 2024

7. Exact Vertex Migration Model of Graph Partitioning Based on Mixed 0–1 Linear Programming and Iteration Algorithm

   Graph partitioning problem is a classical NP-hard problem. The improvement of graph partitioning results by vertex migration is an important class of...

   Zheng-** Yang, Zhi-Peng Jiang, ... Sui-**ang Gao in Journal of the Operations Research Society of China

   Article 24 January 2024
   

8. Every graph is homeomorphic to an antimagic bipartite graph

   Joaquín Tey, Ilan A. Goldfeder, Nahid Y. Javier-Nol in Boletín de la Sociedad Matemática Mexicana

   Article 20 May 2024
   

9. Balanced graph partitioning based on mixed 0-1 linear programming and iteration vertex relocation algorithm

   Graph partitioning is a classical NP problem. The goal of graphing partition is to have as few cut edges in the graph as possible. Meanwhile, the...

   Zhengxi Yang, Zhipeng Jiang, ... Suixiang Gao in Journal of Combinatorial Optimization

   Article 15 June 2023
   

10. Odd Chromatic Number of Graph Classes

    A graph is called odd (respectively, even) if every vertex has odd (respectively, even) degree. Gallai proved that every graph can be partitioned...

    Rémy Belmonte, Ararat Harutyunyan, ... Nikolaos Melissinos in Graph-Theoretic Concepts in Computer Science

    Conference paper 2023
    

11. Factorisation of the Complete Bipartite Graph into Spanning Semiregular Factors

    We enumerate factorisations of the complete bipartite graph into spanning semiregular graphs in several cases, including when the degrees of all the...

    Mahdieh Hasheminezhad, Brendan D. McKay in Annals of Combinatorics

    Article 29 January 2023
    

12. A 2-Bisection with Small Number of Monochromatic Edges of a Claw-Free Cubic Graph

    A bisection of a graph G is a partition of its vertex set into two parts of the same cardinality. A k -bisection of G is a bisection of G such that...

    Seungjae Eom, Kenta Ozeki in Graphs and Combinatorics

    Article Open access 27 January 2023
    

13. Defining an Affine Partition Algebra

    We define an affine partition algebra by generators and relations and prove a variety of basic results regarding this new algebra analogous to those...

    Samuel Creedon, Maud De Visscher in Algebras and Representation Theory

    Article Open access 02 February 2023

14. A polynomial time algorithm for finding a minimum 4-partition of a submodular function

    Tsuyoshi Hirayama, Yuhao Liu, ... Chao Xu in Mathematical Programming

    Article 06 December 2023
    

15. The Rhodes semilattice of a biased graph

    Michael J. Gottstein, Thomas Zaslavsky in Aequationes mathematicae

    Article 15 May 2024

16. Affine Stresses: The Partition of Unity and Kalai’s Reconstruction Conjectures

    Isabella Novik, Hailun Zheng in Discrete & Computational Geometry

    Article 12 April 2024

17. A partition statistic for partitions with even parts distinct

    Andrews, Hirschhorn, and Sellers studied the partition function ped ( n ) which enumerates the number of partitions of n with even parts distinct, and...

    Robert X. J. Hao in Monatshefte für Mathematik

    Article 26 December 2022
    

18. The multiset partition algebra

    Sridhar Narayanan, Digjoy Paul, Shraddha Srivastava in Israel Journal of Mathematics

    Article 28 November 2022

19. Schmidt-type theorems via weighted partition identities

    A 1999 theorem of F. Schmidt states that the number of partitions into distinct parts such that the odd indexed parts sum to n , is equal to the...

    Krishnaswami Alladi in The Ramanujan Journal

    Article 14 September 2022

20. Graph coloring and semidefinite rank

    This paper considers the interplay between semidefinite programming, matrix rank, and graph coloring. Karger et al. (J ACM 45(2):246–265, 1998) give...

    Renee Mirka, Devin Smedira, David P. Williamson in Mathematical Programming

    Article 24 April 2024