Minimal Degree and (k, m)-Pancyclic Ordered Graphs
نویسندگان
چکیده
Given positive integers k £ m £ n, a graph G of order n is (k, m)-pancyclic ordered if for any set of k vertices of G and any integer r with m £ r £ n, there is a cycle of length r encountering the k vertices in a specified order. Minimum degree conditions that imply a graph of sufficiently large order n is (k, m)-pancylic ordered are proved. Examples showing that these constraints are best possible are also provided.
منابع مشابه
Minimum Degree Conditions for Cycles Including Specified Sets of Vertices
This paper generalises the concept of vertex pancyclic graphs. We define a graph as set-pancyclic if for every set S of vertices there is a cycle of every possible length containing S. We show that if the minimum degree of a graph exceeds half its order then the graph is set-pancyclic. We define a graph as k-ordered-pancyclic if, for every set S of cardinality k and every cyclic ordering of S, ...
متن کاملGeneralizing Pancyclic and k-Ordered Graphs
Given positive integers k m n, a graphG of order n is ðk;mÞ-pancyclic if for any set of k vertices of G and any integer r with m r n, there is a cycle of length r containing the k vertices. Minimum degree conditions and minimum sum of degree conditions of nonadjacent vertices that imply a graph is ðk;mÞ-pancylic are proved. If the additional property that the k vertices must appear on the cycle...
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 کاملPancyclicity mod k of claw-free graphs and K1, 4-free graphs
For any natural number k, a graph G is said to be pancyclic mod k if it contains a cycle of every length modulo k. In this paper, we show that every K1,4-free graph G with minimum degree δ(G) ≥ k+ 3 is pancyclic mod k and every claw-free graph G with δ(G) ≥ k+ 1 is pancyclic mod k, which confirms Thomassen’s conjecture [8] for claw-free graphs.
متن کاملPancyclic graphs and linear forests
Given integers k, s, t with 0 ≤ s ≤ t and k ≥ 0, a (k, t, s)-linear forest F is a graph that is the vertex disjoint union of t paths with a total of k edges and with s of the paths being single vertices. If the number of single vertex paths is not critical, the forest F will simply be called a (k, t)-linear forest. A graph G of order n ≥ k + t is (k, t)-hamiltonian if for any (k, t)-linear fore...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Graphs and Combinatorics
دوره 21 شماره
صفحات -
تاریخ انتشار 2005