1. Minimum Separators and Menger’s Theorem

   • Mouhamad El Joubbeh

   Original Paper 15 May 2023 Article: 61

2. Minimally k-Factor-Critical Graphs for Some Large k

   • Jing Guo
   • Heping Zhang

   Original Paper 15 May 2023 Article: 60

   

3. On Reconfiguration Graphs of Independent Sets Under Token Sliding

   • David Avis
   • Duc A. Hoang

   Original Paper 15 May 2023 Article: 59

   

4. The Tight Bound for the Strong Chromatic Indices of Claw-Free Subcubic Graphs

   • Yuquan Lin
   • Wensong Lin

   Original Paper 11 May 2023 Article: 58

   

5. Upper Bounds on the Chromatic Polynomial of a Connected Graph with Fixed Clique Number

   • Shude Long
   • Han Ren

   Original Paper 04 May 2023 Article: 57

6. Paths are Turán-good

   • Dániel Gerbner

   Original Paper Open access 03 May 2023 Article: 56

7. The Connectedness of the Friends-and-Strangers Graph of a Lollipop and Others

   • Lanchao Wang
   • Yaojun Chen

   Original Paper 24 April 2023 Article: 55

8. Gallai–Ramsey Numbers Involving a Rainbow 4-Path

   • Jinyu Zou
   • Zhao Wang
   • Yaping Mao

   Original Paper 24 April 2023 Article: 54

9. A New Proof of the Erdős–Simonovits Conjecture on Walks

   • Grigoriy Blekherman
   • Annie Raymond

   Original Paper 20 April 2023 Article: 53

10. Spectral Radius and Fractional Perfect Matchings in Graphs

    • Yingui Pan
    • Chang Liu

    Original Paper 20 April 2023 Article: 52

11. Girth Conditions and Rota’s Basis Conjecture

    • Benjamin Friedman
    • Sean McGuinness

    Original Paper 20 April 2023 Article: 51

    

12. Conflict-Free Connection Number of Graphs with Four Bridges

    • Zhenzhen Li
    • Baoyindureng Wu

    Original Paper 15 April 2023 Article: 50

    

13. Upper Bounds on the Average Number of Colors in the Non-equivalent Colorings of a Graph

    • Alain Hertz
    • Hadrien Mélot
    • Pierre Hauweele

    Original Paper 15 April 2023 Article: 49

    

14. The Explorer–Director Game on Graphs

    • Pat Devlin
    • Erin Meger
    • Polymath REU Participants

    Original Paper 15 April 2023 Article: 48

    

15. The Turán number of directed paths and oriented cycles

    • Wenling Zhou
    • Binlong Li

    Original Paper 08 April 2023 Article: 47

    

16. Three-Color Ramsey Number of an Odd Cycle Versus Bipartite Graphs with Small Bandwidth

    • Chunlin You
    • Qizhong Lin

    Original Paper 06 April 2023 Article: 46

17. Domino Tilings of Aztec Octagons

    • Hyunggi Kim
    • Sangyop Lee
    • Seungsang Oh

    Original Paper 06 April 2023 Article: 45

    

18. The Eulerian Distribution on k-Colored Involutions

    • Jun Ma
    • Frédéric Toumazet
    • Jiaqi Wang

    Original Paper 04 April 2023 Article: 44

    

19. A Tight Linear Bound to the Chromatic Number of \((P_5, K_1+(K_1\cup K_3))\)-Free Graphs

    • Wei Dong
    • Baogang Xu
    • Yian Xu

    Original Paper 04 April 2023 Article: 43

    

20. Non-chromatic-Adherence of the DP Color Function via Generalized Theta Graphs

    • Manh Vu Bui
    • Hemanshu Kaul
    • Seth Thomason

    Original Paper 04 April 2023 Article: 42

    

21. Forbidding Couples of Tournaments and the Erdös–Hajnal Conjecture

    • Soukaina Zayat
    • Salman Ghazal

    Original Paper 04 April 2023 Article: 41

    

22. Shadow Ratio of Hypergraphs with Bounded Degree

    • Attila Jung

    Original Paper Open access 04 April 2023 Article: 40

23. Sieve Methods in Random Graph Theory

    • Yu-Ru Liu
    • J. C. Saunders

    Original Paper 03 April 2023 Article: 39