منابع مشابه
On circuits and pancyclic line graphs
Clark proved that L(G) is hamiltonian if G is a connected graph of order n 2 6 such that deg u + deg v 2 n 1 p(n) for every edge uv of G, where p(n ) = 0 if n is even and p(n) = 1 if n is odd. Here it is shown that the bound n 1 dn) can be decreased to (2n + 1)/3 if every bridge of G is incident with a vertex of degree 1, which is a necessary condition for hamiltonicity of L(G). Moreover, the c...
متن کاملOn k-path pancyclic graphs
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 d...
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...
متن کاملLocally Pancyclic Graphs
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 ...
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ژورنال
عنوان ژورنال: Czechoslovak Mathematical Journal
سال: 1978
ISSN: 0011-4642,1572-9141
DOI: 10.21136/cmj.1978.101566