Strongly pancyclic and dual-pancyclic graphs

• Autorzy: Terry A. McKee
• 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.

Słowa kluczowe

EN

pancyclic graph; cycle extendable; chordal graph; pancyclic matroid; dual-chordal graph

Kategorie tematyczne

• 05C62: Graph representations (geometric and intersection representations, etc.) {For graph drawing, see also }
• 05C45: Eulerian and Hamiltonian graphs
• 05C38: Paths and cycles

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2009
• Tom: 29
• Numer: 1
• Strony: 5-14

Daty

wydano

2009

otrzymano

2007-05-23

poprawiono

2008-11-26

zaakceptowano

2008-11-26

Twórcy

autor

Terry A. McKee

• 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).

Identyfikatory

DOI

10.7151/dmgt.1429