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Discussiones Mathematicae Graph Theory

2015 | 35 | 2 | 271-281
Tytuł artykułu

On k-Path Pancyclic Graphs

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
For integers k and n with 2 ≤ k ≤ n − 1, a graph G of order n is k-path pancyclic if every path P of order k in G lies on a cycle of every length from k + 1 to n. Thus a 2-path pancyclic graph is edge-pancyclic. In this paper, we present sufficient conditions for graphs to be k-path pancyclic. For a graph G of order n ≥ 3, we establish sharp lower bounds in terms of n and k for (a) the minimum degree of G, (b) the minimum degree-sum of nonadjacent vertices of G and (c) the size of G such that G is k-path pancyclic
Słowa kluczowe
EN
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
271-281
Opis fizyczny
Daty
wydano
2015-05-01
otrzymano
2014-01-27
poprawiono
2014-06-25
zaakceptowano
2014-06-25
online
2015-04-18
Twórcy
autor
• Department of Mathematics Western Michigan University Kalamazoo, MI 49008, USA
autor
• Department of Mathematics Western Michigan University Kalamazoo, MI 49008, USA, ping.zhang@wmich.edu
Bibliografia
• [1] Y. Alavi and J.E. Williamson, Panconnected graphs, Studia Sci. Math. Hungar. 10 (1975) 19-22.
• [2] H.C. Chan, J.M. Chang, Y.L. Wang and S.J. Horng, Geodesic-pancyclic graphs, Discrete Appl. Math. 155 (2007) 1971-1978.
• [3] G. Chartrand, F. Fujie and P. Zhang, On an extension of an observation of Hamilton, J. Combin. Math. Combin. Comput., to appear.
• [4] G. Chartrand, A.M. Hobbs, H.A. Jung, S.F. Kapoor and C.St.J.A. Nash-Williams, The square of a block is Hamiltonian connected, J. Combin. Theory (B) 16 (1974) 290-292. doi:10.1016/0095-8956(74)90075-6[Crossref]
• [5] G. Chartrand and S.F. Kapoor, The cube of every connected graph is 1-hamiltonian, J. Res. Nat. Bur. Standards B 73 (1969) 47-48. doi:10.6028/jres.073B.007
• [6] G. Chartrand, L. Lesniak and P. Zhang, Graphs & Digraphs: 5th Edition (Chapman & Hall/CRC, Boca Raton, FL, 2010).
• [7] G.A. Dirac, Some theorems on abstract graphs, Proc. London Math. Soc. 2 (1952) 69-81. doi:10.1112/plms/s3-2.1.69[Crossref]
• [8] R.J. Faudree and R.H. Schelp, Path connected graphs, Acta Math. Acad. Sci. Hun- gar. 25 (1974) 313-319. doi:10.1007/BF01886090[Crossref]
• [9] H. Fleischner, The square of every two-connected graph is Hamiltonian, J. Combin. Theory (B) 16 (1974) 29-34. doi:10.1016/0095-8956(74)90091-4[Crossref]
• [10] C.St.J.A. Nash-Williams, Problem No. 48, in: Theory of Graphs and its Applica- tions, (Academic Press, New York 1968), 367.
• [11] O. Ore, Note on Hamilton circuits, Amer. Math. Monthly 67 (1960) 55. doi:10.2307/2308928[Crossref]
• [12] O. Ore, Hamilton connected graphs, J. Math. Pures Appl. 42 (1963) 21-27.
• [13] B. Randerath, I. Schiermeyer, M. Tewes and L. Volkmann, Vertex pancyclic graphs, Discrete Appl. Math. 120 (2002) 219-237. doi:10.1016/S0166-218X(01)00292-X[Crossref]
• [14] M. Sekanina, On an ordering of the set of vertices of a connected graph, Publ. Fac. Sci. Univ. Brno 412 (1960) 137-142.
• [15] J.E. Williamson, Panconnected graphs II , Period. Math. Hungar. 8 (1977) 105-116. doi:10.1007/BF02018497 [Crossref]
Typ dokumentu
Bibliografia
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