Báo cáo toán học: " Degree constrained orientations in countable graphs" pps

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Ngày tải lên: 05/08/2014, 15:20

... matchings and Hamiltonian cycles in random graphs. Annals of Discrete Mathematics 28 (1985) 23-46. [6] B. Bollob´as, T.I. Fenner and A.M. Frieze. An algorithm for finding Hamilton cycles in random graphs. ... Cooper. 1-pancyclic Hamilton cycles in random graphs. Random Structures and Algorithms 3.3 (1992) 277-287 [9] C. Cooper and A. Frieze. Pancyclic random graphs....

Ngày tải lên: 07/08/2014, 06:20

... chordless. The length |C| of a cycle C is the number of its edges. The length (B) of a cycle basis B is sum of the lengths of its cycles: (B)=  C∈B |C|.Aminimal cycle basis is a cycle basis with minimal ... . 5. Minimal Cycle Bases of Outerplanar Graphs Let (G, V ) be a 2-connected outerplanar graph. The set T = H \{(1,n)} is a spanning tree of G(V,E). The fun...

Ngày tải lên: 07/08/2014, 06:22

... edge-disjoint one factors and the existence of k -factors in complete multipartite graphs, Discrete Math. 160 (1996) 177–187. [5] T. Niessen and B. Randerath, Regular factors of simple regular graphs ... Theorems, Jahresber. Deutsch. Math Verein. 97 (1995) 19–42. the electronic journal of combinatorics 11 (2004), #R7 7 On regular factors in regular graphs with smal...

Ngày tải lên: 07/08/2014, 08:20

... , proving (8). Inequality (9) follows easily, since, in fact, for every p>3, the function g (x)hasa local minimum at 0. ✷ 5 H-free graphs In this section we are going to prove the following ... (5), we obtain that (r −1)  n p +1  +  2n p +1  <n. Letting n →∞, we see that p ≥ r, contradicting the assumption and completing the proof. ✷ Maximizing independently each summand in...

Ngày tải lên: 07/08/2014, 08:20

... 1-factor F containing e  and thus F is the 1-factor avoiding e. the electronic journal of combina torics 12 (2005), #N23 2 Pan-factorial Property in Regular Graphs ∗ M. Kano 1 and Qinglin Yu 23 1 Department ... 1-factor containing e,so does G ∗ . By Theorem 1, G ∗ has a k-factor containing e and another k-factor avoiding e for all k,1≤ k ≤ 2r − 1. Deleting the matching M from G ∗ ,weo...

Ngày tải lên: 07/08/2014, 08:22

... maximum lengh of a cycle in unit circulant graphs on a Dedekind domain quotiented by an ideal with r distinct maximal factors. Dedekind domains are exactly those integral domains in which every ideal ... have a new induced k-cycle in X n , since we have not changed the coincidences between any of the rows in C. We now use the Observation 2.5 to define isomorphisms between induced...

Ngày tải lên: 07/08/2014, 13:21

... x. For example, for f : x → x 2 we have e f (F )=e (F ); thus e f (F ) can be viewed as a generalization of the size of F . Define ex f (n, F ) to be the maximal value of e f (G)overallF -free ... rate of growth of f. For example, if f grows so fast that e f (G) is dominated by the contribution from the vertices of degree n − 1, then the conclusion of T...

Ngày tải lên: 07/08/2014, 13:21

... sides of a flat face of G  . Proof. This is a corollary of Lemma 9. The notion of the pseudo–embedding may be extended to the representations of a graph on the sphere and to the proper toroidal representations. ... G 1 and G 2 in the embedding of G. G 1 is completely embedded in one of the faces of G 2 and vice versa, which is not possible by convexity of faces and...

Ngày tải lên: 07/08/2014, 13:21

... n-e.c. block-intersection graphs are necessarily simple. Further, we determine all BIBD( v, 3, 2) which have 2-e.c. block-intersection graphs, noting that there are no BIBD( v, 3, 2) with n-e.c. block-intersection ... incomplete block designs (BIBDs) and when their block-intersection graphs are n-existentially closed. We characterise the BIBDs with block size k  3 and index λ = 1...

Ngày tải lên: 07/08/2014, 15:23

... These are orientations where the in -degree function, i.e. the function count- ing the number of ingoing edges at each vertex, satisfies given lower and upper bounds. Degree constrained orientations ... Robbins’ theorem on strongly connected orientations. We mention also Thomassen [11] who raised some related conjectures. In this paper, we will focus on degree constrained o...

Ngày tải lên: 07/08/2014, 21:20

... that in Lemma 4, below, we need to use three extra columns to ‘connect’ two corner-avoiding minimal percolating sets. The next lemma explains our interest in corner-avoiding minimal percolating sets. Lemma ... a minimal percolating set (MinPS) if A percolates in r-neighbour bootstrap percolation, but no proper subset of A percolates. Clearly a percolating set of minimal si...

Ngày tải lên: 07/08/2014, 21:21

... distinguishing chromatic number of K n,n − M We denote by K n,n − M the graph obtained from the complete bipartite graph K n,n by deleting the edges of a perfect matching. This graph arises in the proof of ... c(b k−1 ) = ∆. Let S ⊆ V (G) consist of the union of all the vertices in levels 0 through k − 1 of T . Because of our choice of C and r, G[S] ∼ = T [S], with a ll le...

Ngày tải lên: 07/08/2014, 21:21

... have an embedding of H in G, completing the proof. ✷ To complete the proof o f Theorem 1.1, we only need to apply the f ollowing classi- cal result of Erd˝os [10] regarding the extremal number ... v t v 1 v 2 }. On the other hand, C 4 , C 6 and C 10 do not admit k-partite representations for any k. The importance of these considerations lies in the following theorem. T...

Ngày tải lên: 08/08/2014, 12:22

... a 1 , . . . , a p can be embedded in any graph containing at least  p i=1 (a i + 1) vertices and having minimum degree at least  p i=1 a i . 1 Introduction It is a folklore fact that every tree ... induction on p, the number of trees in the forest. We can assume that every tree in a forest has at least two vertices, so a i ≥ 1. The Base Case, p = 1. The forest in...

Ngày tải lên: 08/08/2014, 14:23