The Upper Bound on the Eulerian Recurrent Lengths of Complete Graphs Obtained by an IP Solver

Shuji Jinbo, Akira Maruoka

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

If the degree of every vertex of a connected graph is even, then the graph has a circuit that contains all of edges, namely an Eulerian circuit. If the length of a shortest subcycle of an Eulerian circuit of a given graph is the largest, then the length is called the Eulerian recurrent length of the graph. For an odd integer n greater than or equal to 3, e(n) denotes the Eulerian recurrent length of the complete graph with n vertices. Values e(n) for all odd integers n with have been found by verification experiments using computers. If n is 7, 9, 11, or 13, then holds, for example. On the other hand, it has been shown that holds for any odd integer n greater than or equal to 15 in previous researches. In this paper, it is proved that holds for every odd integer n greater than or equal to 15. In the core part of the proof of the main theorem, an IP (integer programming) solver is used as the amount of computation is too large to be solved by hand.

Original languageEnglish
Title of host publicationWALCOM
Subtitle of host publicationAlgorithms and Computation - 13th International Conference, WALCOM 2019, Proceedings
EditorsShin-ichi Nakano, Gautam K. Das, Partha S. Mandal, Krishnendu Mukhopadhyaya
PublisherSpringer Verlag
Pages199-208
Number of pages10
ISBN (Print)9783030105631
DOIs
Publication statusPublished - Jan 1 2019
Event13th International Conference and Workshop on Algorithms and Computations, WALCOM 2019 - Guwahati, India
Duration: Feb 27 2019Mar 2 2019

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11355 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference13th International Conference and Workshop on Algorithms and Computations, WALCOM 2019
CountryIndia
CityGuwahati
Period2/27/193/2/19

Fingerprint

Integer programming
Integer Programming
Complete Graph
Odd
Upper bound
Integer
Networks (circuits)
Graph in graph theory
Computer Experiments
Connected graph
Denote
Vertex of a graph
Experiments
Theorem

Keywords

  • Complete graphs
  • Computer experiments
  • Eulerian circuits
  • Graph theory
  • Shortest subcycles

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Jinbo, S., & Maruoka, A. (2019). The Upper Bound on the Eulerian Recurrent Lengths of Complete Graphs Obtained by an IP Solver. In S. Nakano, G. K. Das, P. S. Mandal, & K. Mukhopadhyaya (Eds.), WALCOM: Algorithms and Computation - 13th International Conference, WALCOM 2019, Proceedings (pp. 199-208). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11355 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-030-10564-8_16

The Upper Bound on the Eulerian Recurrent Lengths of Complete Graphs Obtained by an IP Solver. / Jinbo, Shuji; Maruoka, Akira.

WALCOM: Algorithms and Computation - 13th International Conference, WALCOM 2019, Proceedings. ed. / Shin-ichi Nakano; Gautam K. Das; Partha S. Mandal; Krishnendu Mukhopadhyaya. Springer Verlag, 2019. p. 199-208 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11355 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Jinbo, S & Maruoka, A 2019, The Upper Bound on the Eulerian Recurrent Lengths of Complete Graphs Obtained by an IP Solver. in S Nakano, GK Das, PS Mandal & K Mukhopadhyaya (eds), WALCOM: Algorithms and Computation - 13th International Conference, WALCOM 2019, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 11355 LNCS, Springer Verlag, pp. 199-208, 13th International Conference and Workshop on Algorithms and Computations, WALCOM 2019, Guwahati, India, 2/27/19. https://doi.org/10.1007/978-3-030-10564-8_16
Jinbo S, Maruoka A. The Upper Bound on the Eulerian Recurrent Lengths of Complete Graphs Obtained by an IP Solver. In Nakano S, Das GK, Mandal PS, Mukhopadhyaya K, editors, WALCOM: Algorithms and Computation - 13th International Conference, WALCOM 2019, Proceedings. Springer Verlag. 2019. p. 199-208. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-030-10564-8_16
Jinbo, Shuji ; Maruoka, Akira. / The Upper Bound on the Eulerian Recurrent Lengths of Complete Graphs Obtained by an IP Solver. WALCOM: Algorithms and Computation - 13th International Conference, WALCOM 2019, Proceedings. editor / Shin-ichi Nakano ; Gautam K. Das ; Partha S. Mandal ; Krishnendu Mukhopadhyaya. Springer Verlag, 2019. pp. 199-208 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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