A tree decomposition of graph G=(V, E) is referred to as a partition of edge set E into edge-disjoint trees. Given (not necessarily distinct) vertices u-1, u-2...u-k∈V with k≥2, a sufficient and necessary condition ...
Partially supported by tbe National Natural Science Foundation of China ;the Special Science Foundation of the State Education Commission of China.
There have been considerable studies on 'fractals' and their properties. Most of themare concentrated on the properties of sets and measures in R^d. Recently there hasbeen some interest in fractal subsets of Z^d.
A large set of disjoint Mendelsohn triple systems of order v on X={1, 2, …, v} and LMTS(v)={(X, B_i)}_i is called quasi-symmetric (QLMTS(v)), if there exist a, b∈X (a≠b) such that <a, b, i>∈B_i, if and only ...
Definition 1. Let G be a finite group, S G╲{1}and S-1={s-1|s∈G}=S. The Cayley graph on G with respect to S, written as Γ(S; G), is defined as V(Γ(S; G)), E(Γ(S; G)={g, sg)|g∈G, s...
Let X be a set of v elements (v≥3). A transitive triple from X is a collection of three ordered pairs (x, y), (y, z)and (x, z), where x, y and z are distinct dements of X. It is denoted by (x, y, z). A transitive tri...
All graphs considered here are undirected and finite, without loops or multiple edges. Let δ(G)denote the minimum degree of a graph G. A graph G is called Ore-type-(k)(where k is an integer) if d(u)+d(v)≥|V(G)|+k fo...
Let G = ( V, E ) be a simple connected graph of order p, and n be a positive integer. The nth power G^n of G is defined as: V(G)= V(G^n), E(G^n)={uv: u, v ∈ V(G), d_G(u, v)≤n},where d_G,(u, v )is the distance betwee...
Let X(t)(t∈ R^N)be a d-dimensional fractional Brownian motion, x∈R^d is called a multiple point of multiplicity k of X(t)(t∈R^N), if there exist distinct t_l,… ,t_k ∈ RN such
A Mendelsohn triple system on a set X is a pair(X, B), where B is a collection of cyclically ordered triples of distinct elements from X such that each ordered pair of distinct elements from X is covered by a unique t...
For an MTS(v)=(S,(?)), if there exists a,b∈S(a≠b) such that 〈a, b, x〉∈(?)〈b,a,x〉∈(?) and 〈a,x,y〉∈(?)〈b,y,x〉∈(?)(x,y∈S\{a,b}) then we call MTS(v) a symmetric Mendelsohn triple system of order v and denot...