Báo cáo toán học: "Minimal Cycle Bases of Outerplanar Graphs" ppsx

... 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

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... contains no 3 or 5 cycles. Let ¯ d be the average degree of vertices of G.Then α(G) ≥  n ¯ d/2. Proof. Since G contains no 3 or 5 cycles, we have α(G) ≥ d 1 (v) (consider the neighbors of v)andα(G) ... 2 − ( k−1 k ) n k−1 k d 1 k . Proof. Immediate from Theorem 3. This improves Denley’s Theorem 4. References 1. Denley, T., The Independence number of graphs with large odd girth, The E...

Ngày tải lên: 07/08/2014, 06:20

... edge-connectivity of a graph G is the size of a smallest odd edge cut of G.The odd girth of G is the length of a shortest odd cycle of G. Zhang [19] proposed a strengthing of Jaeger’s conjecture, ... thread of length at least 2k). Let v, e, f be the numbers of vertices, edges and faces of G respectively. Since each facial cycle of G has length at least 8k − 3, and th...

Ngày tải lên: 07/08/2014, 06:22

... to the set of arcs of a base circle, such that adjacent vertices of G are mapped to intersecting arcs. The width (in a representation) of a point P of the base circle is the number of representing ... .Thewidth of  is the maximum width of the points of the base circle. (This is not the maximum number of pairwise intersecting arcs.) The arc-width of a g raph G is the min...

Ngày tải lên: 07/08/2014, 06:22

... components of a lattice are intervals of that lattice. For graph theorists it may be of interest that the ordinal decomposition of a poset into indecomposable summands corresponds to the partition of ... w C (n − 1). The set P 1 of all maximal elements in a finite poset P is called the first level of P .One recursively defines the i-th level P i of P to be the first level of the...

Ngày tải lên: 07/08/2014, 06:23

... Proof of Theorem 1 We will show the two parts of the theorem in separate subsections. 3.1 Proof of part I Observe, that since we are looking for a spanning regular subgraph, the f function of Proposition ... electronic journal of combinatorics 14 (2007), #N21 2 3.2 Proof of part II For proving part II of the theorem we want to construct a class of balanced bipartite graphs the...

Ngày tải lên: 07/08/2014, 15:22

... 1)d x y − n(n + 1)y = 0 . (130) The proof of Theorem 4 mimics the steps of the (3, 1)-case. The analogues of the first two identities in Lemma 1 and Lemma 2 of the (3, 1)-case are now as follows: Lemma ... indicating an extraordinary amount of cancellation in the expansion of the determinant. The unusual degree of cancellation is a basic property of a large class of Hankel de...

Ngày tải lên: 07/08/2014, 15:22

... journal of combinatorics 16 (2009), #N14 6 • ∆(G) − δ(G) ≤ 2αn. • G has a degree matching of size at least 2αn. In the course of the proof of Lemma 5, we need the following variation of the standard bounds ... e −c(ǫ)n . This will finish the proof as it proves that there is a large degree matching of the vertices of U 1 (and therefore, of the vertices of V ). the electronic j...

Ngày tải lên: 07/08/2014, 21:21