1. J. Akiyama, M. Kano,Factors and Factorizations of Graphs: Proof Techniques in Factor Theory, vol. 2031 ofLecture Notes in Mathematics (Springer Berlin/Heidelberg, 2011)

   Google Scholar 

2. S. Altinakar, G. Caporossi, A. Hertz, A comparison of integer and constraint programming models for the deficiency problem. Comput. Oper. Res.68, 89–96 (2016)

   Article  Google Scholar 

3. S. Altinakar, G. Caporossi, A. Hertz, Symmetry breaking constraints for the minimum deficiency problem. J. Graph Algorithms Appl.21, 195–218 (2017)

   Article  Google Scholar 

4. A. Asratian, C.J. Casselgren, P.A. Petrosyan, Some results on cyclic interval edge colorings of graphs. J. Graph Theory87, 239–252 (2018)

   Article  Google Scholar 

5. A.S. Asratian, C.J. Casselgren, On interval edge colorings of (α,β)-biregular bipartite graphs. Discrete Mathematics307, 1951–1956 (2007)

   Article  Google Scholar 

6. A.S. Asratian, C.J. Casselgren, On path factors of (3,4)-biregular bigraphs. Graphs Comb.24, 405–411 (2008)

   Article  Google Scholar 

7. A.S. Asratian, C.J. Casselgren, P.A. Petrosyan, Cyclic deficiency of graphs. Discrete Appl. Math.266, 171–185 (2019)

   Article  Google Scholar 

8. A.S. Asratian, C.J. Casselgren, J. Vandenbussche, D.B. West, Proper path-factors and interval edge-coloring of (3, 4)-biregular bigraphs. J. Graph Theory61, 88–97 (2009)

   Article  Google Scholar 

9. A.S. Asratian, R.R. Kamalian, Interval colorings of edges of a multigraph (in Russian). Appl. Math. (also arXiv:1401.8079v1)5, 25–34 (1987)

   Google Scholar 

10. J.J. Bartholdi, K.L. McCroan, Scheduling interviews for a job fair. Operations Research38, 951–960 (1990)

    Article  Google Scholar 

11. M. Bodur, J.R. Luedtke, Integer programming formulations for minimum deficiency interval coloring. Networks72, 249–271 (2018)

    Article  Google Scholar 

12. M. Bouchard, A. Hertz, G. Desaulniers, Lower bounds and a tabu search algorithm for the minimum deficiency problem. J. Comb. Optim.17, 168–191 (2009)

    Article  Google Scholar 

13. C.J. Casselgren, A note on path factors of (3, 4)-biregular bigraphs. Electron. J. Comb.18, 1–12 (2011)

    Google Scholar 

14. C.J. Casselgren, P.A. Petrosyan, B. Toft, On interval and cyclic interval edge colorings of (3,5)-biregular graphs. Discrete Mathematics340, 2678–2687 (2017)

    Article  Google Scholar 

15. C.J. Casselgren, B. Toft, On interval edge colorings of biregular bipartite graphs with small vertex degrees. J. Graph Theory80, 83–97 (2015)

    Article  Google Scholar 

16. E.G. Coffman Jr., D. Dereniowski, W. Kubiak, An efficient algorithm for finding ideal schedules. Acta Informatica49, 1–14 (2012)

    Article  Google Scholar 

17. E. Cole, K. Ost, S. Schirra, Edge-coloring Bipartite Multigraphs in\(O(E \log D)\). Combinatorica21, 5–12 (2001)

    Google Scholar 

18. D. de Werra, Ph. Solot, Compact cylindrical chromatic scheduling. SIAM J. Disc. Math.4, 528–534 (1991)

    Article  Google Scholar 

19. D. de Werra, Ph. Solot, Some graph-theoretical models for scheduling in automated production systems. Networks23, 651–660 (1993)

    Article  Google Scholar 

20. S. Even, A. Itai, A. Shamir, On the complexity of timetable and multicommodity flow problems. SIAM J. Comput.5, 691–703 (1976)

    Article  Google Scholar 

21. K. Giaro, The complexity of consecutive Δ-coloring of bipartite graphs: 4 is easy, 5 is hard. Ars Combin.47, 287–298 (1997)

    Google Scholar 

22. K. Giaro,Compact task scheduling on dedicated processors with no waiting periods. PhD thesis, Gdańsk University of Technology, EIT Faculty, 1999

    Google Scholar 

23. K. Giaro, M. Kubale, M. Małafiejski, Compact scheduling in open shop with zero-one time operations. INFOR37, 37–47 (1999)

    Google Scholar 

24. K. Giaro, M. Kubale, M. Małafiejski, On the deficiency of bipartite graphs. Discrete Appl. Math.94, 193–203 (1999)

    Article  Google Scholar 

25. K. Giaro, M. Kubale, M. Małafiejski, Consecutive colorings of the edges of general graphs. Discrete Mathematics236, 131–143 (2001)

    Article  Google Scholar 

26. T. Gonzalez, Unit execution time shop problems. Math. O. R7, 57–66 (1982)

    Article  Google Scholar 

27. A. Grzesik, H. Khachatrian, Interval edge-coloring ofK_1,m,n. Discrete Appl. Math.174, 140–145 (2014)

    Article  Google Scholar 

28. R.W. Hall, Cyclic scheduling for improvement. Int. J. Prod. Res.26, 457–472 (1988)

    Article  Google Scholar 

29. H.M. Hansen, Scheduling with minimum waiting periods (in Danish). Master’s thesis, Odense University, Denmark, 1992

    Google Scholar 

30. D. Hanson, C.O.M. Loten, A lower bound for interval coloring bi-regular bipartite graphs. Bull. Inst. Comb. Appl.18, 69–74 (1996)

    Google Scholar 

31. D. Hanson, C.O.M. Loten, B. Toft, On interval colourings of bi-regular bipartite graphs. Ars Comb.50, 23–32 (1998)

    Google Scholar 

32. T.R. Jensen, B. Toft,Graph Coloring Problems (Wiley, 1995)

    Google Scholar 

33. R.R. Kamalian, Interval colorings of complete bipartite graphs and trees. Comput. Cen. of Acad. Sci. of Armenian SSR, Erevan, 1989 (in Russian)

    Google Scholar 

34. R.R. Kamalian,Interval edge-colorings. PhD thesis, Novosibirsk, 1990

    Google Scholar 

35. H.H. Khachatrian, T. Mamikonyan, On interval edge-colorings of bipartite graphs of small order. arXiv:1508.02851v1, 2015

    Google Scholar 

36. A.V. Kostochka, Unpublished manuscript (1995)

    Google Scholar 

37. M. Kubale, Some results concerning the complexity of restricted coloring of graphs. Discrete Appl. Math.36, 35–46 (1992)

    Article  Google Scholar 

38. M. Kubale, A. Nadolski, Chromatic scheduling in a cyclic open shop. Eur. J. Oper. Res.164, 585–591 (2005)

    Article  Google Scholar 

39. W. Kubiak,Proportional Optimization and Fairness (Springer, 2009)

    Google Scholar 

40. N.V.R. Mahadev, Ph. Solot, D. de Werra, The cyclic compact open-shop scheduling problem. Discrete Mathematics111, 361–366 (1993)

    Article  Google Scholar 

41. S. Micali, V.V. Vazirani, An\(O(m\sqrt {n})\) algorithm for finding maximum matching in general graphs, inProc. 21st Ann. IEEE Symp. on Foundations of Computer Science, pp. 17–27 (1980)

    Google Scholar 

42. Y. Monden,Toyota Production System: An Integrated Approach to Just–In–Time (Engineering and Management Press, Norcross, GA, 1998)

    Google Scholar 

43. A. Nadolski, Compact cyclic edge-colorings of graphs. Discrete Mathematics308, 2407–2417 (2008)

    Article  Google Scholar 

44. J. Petersen, Die teorie der regul\(\ddot {a}\)ren graphs. Acta Math., 193–220 (1891)

    Google Scholar 

45. P.A. Petrosyan, H.H. Khachatrian, Interval non-edge-colorable bipartite graphs and multigraphs. J. Graph Theory76, 200–216 (2014)

    Article  Google Scholar 

46. M.D. Plummer, Graph factors and factorization:1985 - 2003: A survey. Discrete Mathematics307, 791–821 (2007)

    Article  Google Scholar 

47. A.V. Pyatkin, Interval coloring of (3,4)-biregular bipartite graphs having large cubic subgraphs. J. Graph Theory47, 122–128 (2004)

    Article  Google Scholar 

48. A. Schwartz, The deficiency of a regular graph. Discrete Mathematics306, 1947–1954 (2006)

    Article  Google Scholar 

49. S.V. Sevast’janov, Interval colorability of the edges of a bipartite graph (in Russian). Met. Diskret Analiz.50, 61–72 (1990)

    Google Scholar 

50. Z. Shao, Z. Li, B. Wang, S. Wang, X. Zhang, Interval edge-coloring: A model of curriculum scheduling. AKCE Int. J. Graphs Comb.17, 725–729 (2020)

    Article  Google Scholar 

51. F. Yang, X. Li, Interval coloring of (3,4)-biregular graphs having two (2,3)-biregular subgraphs. Appl. Math. Lett.24, 1574–1577 (2011)

    Article  Google Scholar 

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