منابع مشابه
Edge-pancyclic block-intersection graphs
Alspach, B. and D. Hare, Edge-pancyclic block-intersection graphs, Discrete Mathematics 97 (1991) 17-24. It is shown that the block-intersection graph of both a balanced incomplete block design with block size at least 3 and A = 1, and a transversal design is edge-pancyclic.
متن کاملStrongly pancyclic and dual-pancyclic graphs
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 ar...
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We prove the following theorem. Let G be a graph of order n and let W V(G). If |W | 3 and dG(x)+dG( y) n for every pair of non-adjacent vertices x, y # W, then either G contains cycles C , C, ..., C |W | such that C i contains exactly i vertices from W (i=3, 4, ..., |W | ), or |W |=n and G=Kn 2, n 2 , or else |W |=4, G[W]=K2, 2 . This generalizes a result of J. A. Bondy (1971, J. Combin. Theory...
متن کاملGeodesic-pancyclic graphs
A shortest path connecting two vertices u and v is called a u-v geodesic. The distance between u and v, denoted by dG(u, v), is the number of edges in a u-v geodesic. A graph G with n vertices is geodesic-pancyclic if for each pair of vertices u, v ∈ V (G), every u-v geodesic lies on every cycle of length k satisfying max{2dG(u, v), 3} ≤ k ≤ n. In this paper, we study the properties for graphs ...
متن کاملVertex Pancyclic Graphs
Let G be a graph of order n. A graph G is called pancyclic if it contains a cycle of length k for every 36 k6 n, and it is called vertex pancyclic if every vertex is contained in a cycle of length k for every 36 k6 n. In this paper, we shall present di0erent su1cient conditions for graphs to be vertex pancyclic. ? 2002 Elsevier Science B.V. All rights reserved.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1991
ISSN: 0012-365X
DOI: 10.1016/0012-365x(91)90417-z