Split graph (English Wikipedia)

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Földes & Hammer (1977a) had a more general definition, in which the graphs they called split graphs also included bipartite graphs (that is, graphs that be partitioned into two independent sets) and the complements of bipartite graphs (that is, graphs that can be partitioned into two cliques). Földes & Hammer (1977b) use the definition given here, which has been followed in the subsequent literature; for instance, it is Brandstädt, Le & Spinrad (1999), Definition 3.2.3, p.41. Földes, Stéphane; Hammer, Peter Ladislaw (1977a), "Split graphs", Proceedings of the Eighth Southeastern Conference on Combinatorics, Graph Theory and Computing (Louisiana State Univ., Baton Rouge, La., 1977), Congressus Numerantium, vol. XIX, Winnipeg: Utilitas Math., pp. 311–315, MR 0505860. Földes, Stéphane; Hammer, Peter Ladislaw (1977b), "Split graphs having Dilworth number two", Canadian Journal of Mathematics, 29 (3): 666–672, doi:10.4153/CJM-1977-069-1, MR 0463041. Brandstädt, Andreas; Le, Van Bang; Spinrad, Jeremy (1999), Graph Classes: A Survey, SIAM Monographs on Discrete Mathematics and Applications, ISBN 0-89871-432-X.
Földes & Hammer (1977a); Golumbic (1980), Theorem 6.3, p. 151. Földes, Stéphane; Hammer, Peter Ladislaw (1977a), "Split graphs", Proceedings of the Eighth Southeastern Conference on Combinatorics, Graph Theory and Computing (Louisiana State Univ., Baton Rouge, La., 1977), Congressus Numerantium, vol. XIX, Winnipeg: Utilitas Math., pp. 311–315, MR 0505860. Golumbic, Martin Charles (1980), Algorithmic Graph Theory and Perfect Graphs, Academic Press, ISBN 0-12-289260-7, MR 0562306.
Golumbic (1980), Theorem 6.1, p. 150. Golumbic, Martin Charles (1980), Algorithmic Graph Theory and Perfect Graphs, Academic Press, ISBN 0-12-289260-7, MR 0562306.
Földes & Hammer (1977a); Golumbic (1980), Theorem 6.3, p. 151; Brandstädt, Le & Spinrad (1999), Theorem 3.2.3, p. 41. Földes, Stéphane; Hammer, Peter Ladislaw (1977a), "Split graphs", Proceedings of the Eighth Southeastern Conference on Combinatorics, Graph Theory and Computing (Louisiana State Univ., Baton Rouge, La., 1977), Congressus Numerantium, vol. XIX, Winnipeg: Utilitas Math., pp. 311–315, MR 0505860. Golumbic, Martin Charles (1980), Algorithmic Graph Theory and Perfect Graphs, Academic Press, ISBN 0-12-289260-7, MR 0562306. Brandstädt, Andreas; Le, Van Bang; Spinrad, Jeremy (1999), Graph Classes: A Survey, SIAM Monographs on Discrete Mathematics and Applications, ISBN 0-89871-432-X.
McMorris & Shier (1983); Voss (1985); Brandstädt, Le & Spinrad (1999), Theorem 4.4.2, p. 52. McMorris, F. R.; Shier, D. R. (1983), "Representing chordal graphs on K_1,n", Commentationes Mathematicae Universitatis Carolinae, 24: 489–494, MR 0730144. Voss, H.-J. (1985), "Note on a paper of McMorris and Shier", Commentationes Mathematicae Universitatis Carolinae, 26: 319–322, MR 0803929. Brandstädt, Andreas; Le, Van Bang; Spinrad, Jeremy (1999), Graph Classes: A Survey, SIAM Monographs on Discrete Mathematics and Applications, ISBN 0-89871-432-X.
Földes & Hammer (1977b); Golumbic (1980), Theorem 9.7, page 212. Földes, Stéphane; Hammer, Peter Ladislaw (1977b), "Split graphs having Dilworth number two", Canadian Journal of Mathematics, 29 (3): 666–672, doi:10.4153/CJM-1977-069-1, MR 0463041. Golumbic, Martin Charles (1980), Algorithmic Graph Theory and Perfect Graphs, Academic Press, ISBN 0-12-289260-7, MR 0562306.
Kézdy, Snevily & Wang (1996). Kézdy, André E.; Snevily, Hunter S.; Wang, Chi (1996), "Partitioning permutations into increasing and decreasing subsequences", Journal of Combinatorial Theory, Series A, 73 (2): 353–359, doi:10.1016/S0097-3165(96)80012-4, MR 1370138.
Hammer & Simeone (1981); Golumbic (1980), Theorem 6.2, p. 150. Hammer, Peter Ladislaw; Simeone, Bruno (1981), "The splittance of a graph", Combinatorica, 1 (3): 275–284, doi:10.1007/BF02579333, MR 0637832. Golumbic, Martin Charles (1980), Algorithmic Graph Theory and Perfect Graphs, Academic Press, ISBN 0-12-289260-7, MR 0562306.
Hammer & Simeone (1981); Tyshkevich (1980); Tyshkevich, Melnikow & Kotov (1981); Golumbic (1980), Theorem 6.7 and Corollary 6.8, p. 154; Brandstädt, Le & Spinrad (1999), Theorem 13.3.2, p. 203. Merris (2003) further investigates the degree sequences of split graphs. Hammer, Peter Ladislaw; Simeone, Bruno (1981), "The splittance of a graph", Combinatorica, 1 (3): 275–284, doi:10.1007/BF02579333, MR 0637832. Tyshkevich, Regina I. (1980), "[The canonical decomposition of a graph]", Doklady Akademii Nauk SSSR (in Russian), 24: 677–679, MR 0587712 Tyshkevich, Regina I.; Melnikow, O. I.; Kotov, V. M. (1981), "On graphs and degree sequences: the canonical decomposition", Kibernetika (in Russian), 6: 5–8, MR 0689420. Golumbic, Martin Charles (1980), Algorithmic Graph Theory and Perfect Graphs, Academic Press, ISBN 0-12-289260-7, MR 0562306. Brandstädt, Andreas; Le, Van Bang; Spinrad, Jeremy (1999), Graph Classes: A Survey, SIAM Monographs on Discrete Mathematics and Applications, ISBN 0-89871-432-X. Merris, Russell (2003), "Split graphs", European Journal of Combinatorics, 24 (4): 413–430, doi:10.1016/S0195-6698(03)00030-1, MR 1975945.
Hammer & Simeone (1981). Hammer, Peter Ladislaw; Simeone, Bruno (1981), "The splittance of a graph", Combinatorica, 1 (3): 275–284, doi:10.1007/BF02579333, MR 0637832.

archive.org

Földes & Hammer (1977a) had a more general definition, in which the graphs they called split graphs also included bipartite graphs (that is, graphs that be partitioned into two independent sets) and the complements of bipartite graphs (that is, graphs that can be partitioned into two cliques). Földes & Hammer (1977b) use the definition given here, which has been followed in the subsequent literature; for instance, it is Brandstädt, Le & Spinrad (1999), Definition 3.2.3, p.41. Földes, Stéphane; Hammer, Peter Ladislaw (1977a), "Split graphs", Proceedings of the Eighth Southeastern Conference on Combinatorics, Graph Theory and Computing (Louisiana State Univ., Baton Rouge, La., 1977), Congressus Numerantium, vol. XIX, Winnipeg: Utilitas Math., pp. 311–315, MR 0505860. Földes, Stéphane; Hammer, Peter Ladislaw (1977b), "Split graphs having Dilworth number two", Canadian Journal of Mathematics, 29 (3): 666–672, doi:10.4153/CJM-1977-069-1, MR 0463041. Brandstädt, Andreas; Le, Van Bang; Spinrad, Jeremy (1999), Graph Classes: A Survey, SIAM Monographs on Discrete Mathematics and Applications, ISBN 0-89871-432-X.
Földes & Hammer (1977a); Golumbic (1980), Theorem 6.3, p. 151; Brandstädt, Le & Spinrad (1999), Theorem 3.2.3, p. 41. Földes, Stéphane; Hammer, Peter Ladislaw (1977a), "Split graphs", Proceedings of the Eighth Southeastern Conference on Combinatorics, Graph Theory and Computing (Louisiana State Univ., Baton Rouge, La., 1977), Congressus Numerantium, vol. XIX, Winnipeg: Utilitas Math., pp. 311–315, MR 0505860. Golumbic, Martin Charles (1980), Algorithmic Graph Theory and Perfect Graphs, Academic Press, ISBN 0-12-289260-7, MR 0562306. Brandstädt, Andreas; Le, Van Bang; Spinrad, Jeremy (1999), Graph Classes: A Survey, SIAM Monographs on Discrete Mathematics and Applications, ISBN 0-89871-432-X.
McMorris & Shier (1983); Voss (1985); Brandstädt, Le & Spinrad (1999), Theorem 4.4.2, p. 52. McMorris, F. R.; Shier, D. R. (1983), "Representing chordal graphs on K_1,n", Commentationes Mathematicae Universitatis Carolinae, 24: 489–494, MR 0730144. Voss, H.-J. (1985), "Note on a paper of McMorris and Shier", Commentationes Mathematicae Universitatis Carolinae, 26: 319–322, MR 0803929. Brandstädt, Andreas; Le, Van Bang; Spinrad, Jeremy (1999), Graph Classes: A Survey, SIAM Monographs on Discrete Mathematics and Applications, ISBN 0-89871-432-X.
Brandstädt, Le & Spinrad (1999), Corollary 7.1.1, p. 106, and Theorem 7.1.2, p. 107. Brandstädt, Andreas; Le, Van Bang; Spinrad, Jeremy (1999), Graph Classes: A Survey, SIAM Monographs on Discrete Mathematics and Applications, ISBN 0-89871-432-X.
Hammer & Simeone (1981); Tyshkevich (1980); Tyshkevich, Melnikow & Kotov (1981); Golumbic (1980), Theorem 6.7 and Corollary 6.8, p. 154; Brandstädt, Le & Spinrad (1999), Theorem 13.3.2, p. 203. Merris (2003) further investigates the degree sequences of split graphs. Hammer, Peter Ladislaw; Simeone, Bruno (1981), "The splittance of a graph", Combinatorica, 1 (3): 275–284, doi:10.1007/BF02579333, MR 0637832. Tyshkevich, Regina I. (1980), "[The canonical decomposition of a graph]", Doklady Akademii Nauk SSSR (in Russian), 24: 677–679, MR 0587712 Tyshkevich, Regina I.; Melnikow, O. I.; Kotov, V. M. (1981), "On graphs and degree sequences: the canonical decomposition", Kibernetika (in Russian), 6: 5–8, MR 0689420. Golumbic, Martin Charles (1980), Algorithmic Graph Theory and Perfect Graphs, Academic Press, ISBN 0-12-289260-7, MR 0562306. Brandstädt, Andreas; Le, Van Bang; Spinrad, Jeremy (1999), Graph Classes: A Survey, SIAM Monographs on Discrete Mathematics and Applications, ISBN 0-89871-432-X. Merris, Russell (2003), "Split graphs", European Journal of Combinatorics, 24 (4): 413–430, doi:10.1016/S0195-6698(03)00030-1, MR 1975945.

doi.org

Földes & Hammer (1977a) had a more general definition, in which the graphs they called split graphs also included bipartite graphs (that is, graphs that be partitioned into two independent sets) and the complements of bipartite graphs (that is, graphs that can be partitioned into two cliques). Földes & Hammer (1977b) use the definition given here, which has been followed in the subsequent literature; for instance, it is Brandstädt, Le & Spinrad (1999), Definition 3.2.3, p.41. Földes, Stéphane; Hammer, Peter Ladislaw (1977a), "Split graphs", Proceedings of the Eighth Southeastern Conference on Combinatorics, Graph Theory and Computing (Louisiana State Univ., Baton Rouge, La., 1977), Congressus Numerantium, vol. XIX, Winnipeg: Utilitas Math., pp. 311–315, MR 0505860. Földes, Stéphane; Hammer, Peter Ladislaw (1977b), "Split graphs having Dilworth number two", Canadian Journal of Mathematics, 29 (3): 666–672, doi:10.4153/CJM-1977-069-1, MR 0463041. Brandstädt, Andreas; Le, Van Bang; Spinrad, Jeremy (1999), Graph Classes: A Survey, SIAM Monographs on Discrete Mathematics and Applications, ISBN 0-89871-432-X.
Földes & Hammer (1977b); Golumbic (1980), Theorem 9.7, page 212. Földes, Stéphane; Hammer, Peter Ladislaw (1977b), "Split graphs having Dilworth number two", Canadian Journal of Mathematics, 29 (3): 666–672, doi:10.4153/CJM-1977-069-1, MR 0463041. Golumbic, Martin Charles (1980), Algorithmic Graph Theory and Perfect Graphs, Academic Press, ISBN 0-12-289260-7, MR 0562306.
Kézdy, Snevily & Wang (1996). Kézdy, André E.; Snevily, Hunter S.; Wang, Chi (1996), "Partitioning permutations into increasing and decreasing subsequences", Journal of Combinatorial Theory, Series A, 73 (2): 353–359, doi:10.1016/S0097-3165(96)80012-4, MR 1370138.
Hammer & Simeone (1981); Golumbic (1980), Theorem 6.2, p. 150. Hammer, Peter Ladislaw; Simeone, Bruno (1981), "The splittance of a graph", Combinatorica, 1 (3): 275–284, doi:10.1007/BF02579333, MR 0637832. Golumbic, Martin Charles (1980), Algorithmic Graph Theory and Perfect Graphs, Academic Press, ISBN 0-12-289260-7, MR 0562306.
Müller (1996) Müller, Haiko (1996), "Hamiltonian Circuits in Chordal Bipartite Graphs", Discrete Mathematics, 156: 291–298, doi:10.1016/0012-365x(95)00057-4.
Bertossi (1984) Bertossi, Alan A. (1984), "Dominating sets for split and bipartite graphs", Information Processing Letters, 19: 37–40, doi:10.1016/0020-0190(84)90126-1.
Hammer & Simeone (1981); Tyshkevich (1980); Tyshkevich, Melnikow & Kotov (1981); Golumbic (1980), Theorem 6.7 and Corollary 6.8, p. 154; Brandstädt, Le & Spinrad (1999), Theorem 13.3.2, p. 203. Merris (2003) further investigates the degree sequences of split graphs. Hammer, Peter Ladislaw; Simeone, Bruno (1981), "The splittance of a graph", Combinatorica, 1 (3): 275–284, doi:10.1007/BF02579333, MR 0637832. Tyshkevich, Regina I. (1980), "[The canonical decomposition of a graph]", Doklady Akademii Nauk SSSR (in Russian), 24: 677–679, MR 0587712 Tyshkevich, Regina I.; Melnikow, O. I.; Kotov, V. M. (1981), "On graphs and degree sequences: the canonical decomposition", Kibernetika (in Russian), 6: 5–8, MR 0689420. Golumbic, Martin Charles (1980), Algorithmic Graph Theory and Perfect Graphs, Academic Press, ISBN 0-12-289260-7, MR 0562306. Brandstädt, Andreas; Le, Van Bang; Spinrad, Jeremy (1999), Graph Classes: A Survey, SIAM Monographs on Discrete Mathematics and Applications, ISBN 0-89871-432-X. Merris, Russell (2003), "Split graphs", European Journal of Combinatorics, 24 (4): 413–430, doi:10.1016/S0195-6698(03)00030-1, MR 1975945.
Hammer & Simeone (1981). Hammer, Peter Ladislaw; Simeone, Bruno (1981), "The splittance of a graph", Combinatorica, 1 (3): 275–284, doi:10.1007/BF02579333, MR 0637832.