PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2009 | 29 | 1 | 5-14
Tytuł artykułu

Strongly pancyclic and dual-pancyclic graphs

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Say that a cycle C almost contains a cycle C¯ if every edge except one of C¯ is an edge of C. Call a graph G strongly pancyclic if every nontriangular cycle C almost contains another cycle C¯ and every nonspanning cycle C is almost contained in another cycle C⁺. This is equivalent to requiring, in addition, that the sizes of C¯ and C⁺ differ by one from the size of C. Strongly pancyclic graphs are pancyclic and chordal, and their cycles enjoy certain interpolation and extrapolation properties with respect to almost containment. Much of this carries over from graphic to cographic matroids; the resulting 'dual-pancyclic' graphs are shown to be exactly the 3-regular dual-chordal graphs.
Wydawca
Rocznik
Tom
29
Numer
1
Strony
5-14
Opis fizyczny
Daty
wydano
2009
otrzymano
2007-05-23
poprawiono
2008-11-26
zaakceptowano
2008-11-26
Twórcy
  • Department of Mathematics & Statistics, Wright State University, Dayton, Ohio 45435, USA
Bibliografia
  • [1] B. Beavers and J. Oxley, On pancyclic representable matroids, Discrete Math. 305 (2005) 337-343, doi: 10.1016/j.disc.2005.10.008.
  • [2] L. Cai, Spanning 2-trees, in: Algorithms, Concurrency and Knowledge (Pathumthani, 1995) 10-22, Lecture Notes in Comput. Sci. 1023 (Springer, Berlin, 1995).
  • [3] R.J. Faudree, R.J. Gould, M.S. Jacobson and L.M. Lesniak, Degree conditions and cycle extendability, Discrete Math. 141 (1995) 109-122, doi: 10.1016/0012-365X(93)E0193-8.
  • [4] R. Faudree, Z. Ryjácek and I. Schiermeyer, Forbidden subgraphs and cycle extendability, J. Combin. Math. Combin. Comput. 19 (1995) 109-128.
  • [5] K.P. Kumar and C.E. Veni Madhavan, A new class of separators and planarity of chordal graphs, in: Foundations of Software Technology and Theoretical Computer Science (Bangalore, 1989) 30-43, Lecture Notes in Comput. Sci. 405 (Springer, Berlin, 1989).
  • [6] T.A. McKee, Recognizing dual-chordal graphs, Congr. Numer. 150 (2001) 97-103.
  • [7] T.A. McKee, Dualizing chordal graphs, Discrete Math. 263 (2003) 207-219, doi: 10.1016/S0012-365X(02)00577-0.
  • [8] T.A. McKee and F.R. McMorris, Topics in Intersection Graph Theory (Society for Industrial and Applied Mathematics, Philadelphia, 1999), doi: 10.1137/1.9780898719802.
  • [9] J.G. Oxley, Matroidal methods in graph theory, in: Handbook of Graph Theory, Discrete Mathematics and its Applications, J.L. Gross and J. Yellen, eds CRC Press (Boca Raton, FL, 2004) 574-598.
  • [10] M. Yannakakis, Node- and edge-deletion NP-complete problems, Conference Record of the Tenth Annual ACM Symposium on Theory of Computing (San Diego, Calif., 1978), 253-264 (ACM, New York, 1978).
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1429
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.