Báo cáo toán học: "Hamiltonicity of k-Traceable Graphs" pps

... graph P (n) of order n constructed in the proof of Lemma 4.2 is only defined for n ≥ 12 . Next we consider the existence of k-traceable graphs of order k + 1. Skupien [12] calls a graph of order ... achment in C, i.e., A = N C (H 1 ). Let U be the set of successors of vertices of A on C, and let W be the set of predecessors of vertices of A on C. We first note that U and...

Ngày tải lên: 08/08/2014, 14:22

Ngày tải lên: 05/08/2014, 15:20

... reduced form through a series of successive deletions of pairs of letters (not necessarily adjacent). For uw k u −1 , the number of such deletions is the same as the number of letters in u. For any ... an equivalence relation on the set of Coxeter elements, that corresponds precisely to the reacha bility relation on the set of acyclic edge orientations. Proof of theorem 1.1. O...

Ngày tải lên: 08/08/2014, 01:20

... Q be the class of outerplanar graphs, PK k be the family of partial k-trees, P be the class of planar graphs. For a class K of graphs, let −→ K be the set of all orientations of graphs in K. ... chromatic number of graphs. A natural generalization of chromatic number to digraphs was introduced by Neumann -Lara in [21]. A (proper) colouring of a digraph D is a colouring of...

Ngày tải lên: 08/08/2014, 11:20

... increase in the number of edges of the cube of a regular, co nnected graph. Such an increase was already demonstrated by Hegarty in Theorem 2. Here we give an alternative proof of that theorem, yielding ... diameter of G, diam(G), as the minimal r such that G r is complete (alternatively, the maximal distance between two vertices). Denote the number of edges of G by e(G). For v...

Ngày tải lên: 08/08/2014, 14:23

... the proof, we speak of the probability of various events, and evaluate the expected value of some random variables. The underlying probability space for all this is the set of all t-tuples of embeddings ... in terms of random embeddings of pairs of graphs in K n . Theorem 1, discusses random embeddings of t-tuples of graphs. In Theorem 2, we use this to extend Tomescu’s re...

Ngày tải lên: 07/08/2014, 06:20

... application of the ↔-partition of R we derive bounds on the number of distinct minimal cycle bases of G. the electronic journal of combinatorics 7 (2000), #R16 10 ordering of the vertex set V of G.SetV r = ... C. The set C of all generalized cycles forms a subspace of (E, ⊕, ·) which is called the cycle space of G.AbasisB of the cycle space C is called a cycle basis of...

Ngày tải lên: 07/08/2014, 06:20

... description of all mergings of classes of the 2-orbits of the group G 1 of order 200 in its transitive action of degree 100 on the set Ω. This group is naturally described as a subgroup of H,namelyG 1 ∼ = (F 20 5 × ... main target of our interest. On next step of computations we tried group H of order 1200 which is an overgroup of H. By definition, H is the normalizer of...

Ngày tải lên: 07/08/2014, 07:21

... of G is a set of subgraphs G 1 , ,G t such that any edge of G is an edge of exactly one of G 1 , ,G t and all G 1 , ,G t ∈ .Letφ(G, ) denote the minimum size of an -decomposition of G. The main ... non-complete graph of order 4. 1 Introduction Let G be a simple graph with vertex set V and edge set E. The number of vertices of a graph is its order.Thedegree of a vertex v...

Ngày tải lên: 07/08/2014, 13:21