Báo cáo toán học: "Minimum connected dominating sets of random cubic graphs" docx

... theorem. Theorem 1 The size of a minimum connected dominating set of a random n-vertex cubic graph is asymptotically almost surely less than 0.5854n. Proof After the first element of C has been chosen, ... least to within an additive constant, of the main result of [10]. They also showed that the size of a connected dominating set of an n-vertex cubic graph of gir...

Ngày tải lên: 07/08/2014, 06:23

... the colouring of G 1 . the electronic journal of combinatorics 13 (2006), #R77 5 PSfrag replacements α α α α γ γ γ γ γ β β β β Figure 1: The colouring of H used in the second case of the proof of Lemma ... deferred to Section 4. the electronic journal of combinatorics 13 (2006), #R77 2 Let us see now how these two lemmas yield the proof of Theorem 2. Proof of Theorem 2. Note t...

Ngày tải lên: 07/08/2014, 13:21

... automorphism group of unitary Cayley graphs and answer the open question from [23] about the ratio of the size of the automorphism group of X n and the size of the group of a ffine automorphisms of X n . ... morphism group of a graph with square-f ree order and D = {1, p} is the wreath product of the group of class permutations C i and the groups of permutations of verti...

Ngày tải lên: 08/08/2014, 14:22

Ngày tải lên: 05/08/2014, 15:20

... by Lunnon. No proof of Theorem 2.2 will be given because the proof of Theorem 2.2 is ex- tremely similar to the proof of Theorem 2.1 given below. 3 Proof of Theorem 2.1 For ease of notation let ... vector of S n,m . The vector d n is defined differently on two different intervals of coordinates. We call these intervals of coordinates regions of definition. For 1 ≤ i ≤ 2n (the fir...

Ngày tải lên: 07/08/2014, 06:22

... . . , V k } of the vertex set of G is a connected set partition if each sub- graph G[V j ] induced by the blocks V j of π is connected for 1 ≤ j ≤ k. Define q i (G) as the number of connected set ... set (S \ X) ∪ (T \ Y ). The vertex set of one component of the bipartite graph consists of one block of a partition of S \ X and one block of a partition of T \ Y . The...

Ngày tải lên: 08/08/2014, 12:23

... Y. Zhao, Proof of a tiling conjecture of Koml´os, Random Struct. Algorithms 23 (2003), 180–205. [15] M. Simonovits and V. T. S´os, Szemer´edi ’ s partition and q uasi randomness, Random Struct. ... part. We assign a weight of b to each H-subgraph in the decomposition and a weight of 1 to single edges. The total weig ht of the deco mposition is the sum of the weights of all e...

Ngày tải lên: 08/08/2014, 14:23

Ngày tải lên: 05/08/2014, 10:20

... that T be a tree, and also considered cubic forests. And we tried replacing the single values of h i by sets of values (we tried sets of size two). Neither of these modifications produced better ... a comprehensive picture of the state of the art in 1982. In this note, we shall be specifically interested in cubic (trivalent) cages and note that the current status of the pr...

Ngày tải lên: 07/08/2014, 06:20

... corresponding adjacencies) at each of the edge crossings of the particular drawing of G. Is the planar subdivision of any rectilinear drawing of K n necessarily 3 -connected? This question was also posed ... 60. Proof: By way of contradiction, assume that there exists a rectilinear drawing of K 10 with 60 crossings. Since each edge crossing comprises of four vertices, the sum...

Ngày tải lên: 07/08/2014, 06:22