Báo cáo toán học: "Star coloring high girth planar graphs" ppt

... of interconnections and destinations is re- duced. Addressing within a group is also simplified. With one known row-column connection in submatrix, the rest of the submatrix connections could ... varying vertex degrees and girths produce column-weight-two LDPC codes of different girths and rates. For a graph of size n,vertexdegreeofk,andgirthofg, the corresponding LDPC code matrix is of...

Ngày tải lên: 22/06/2014, 22:20

... Denley’s Theorem 4. References 1. Denley, T., The Independence number of graphs with large odd girth, The Electronic Journal of Combinatorics 1 (1994) #R9. 2 We can now prove the following theorem. Theorem ... is sharp for the regular complete bipartite graphs K aa . The above results are readily extended to graphs of larger odd girth. Lemma 2: Let G have odd girth...

Ngày tải lên: 07/08/2014, 06:20

... 68W25. Keywords: graph coloring, online algorithms. Abstract The problem of online coloring an unknown graph is known to be hard. Here we consider the problem of online coloring in the relaxed ... independence number α are known in advance. The unknown case can be handled via a doubling technique, see [5]. Without loss of generality, α ≥ n/ log n.Letq =(1/2) log n/α n. Before colori...

Ngày tải lên: 07/08/2014, 06:20

... tight. The odd 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 ... of length at least 2k. For otherwise, for any internal vertex x of a thread of length the electronic journal of combinatorics 8 (2001), #R25 3 Circular chromati...

Ngày tải lên: 07/08/2014, 06:22

... − 15 + 12 − 3=0 N char(dodecahedron) = 20 − 60 + 20 = −20 2 Computing the Neighborhood Characteristic The neighborhood characteristic of a graph can also be calculated in terms of the complete bipartite ... overcounting is corrected for in the following theorem (which also shows that, for a bipartite graph G, N char(G) equals twice the ‘bipartite characteristic defined in [5]). T...

Ngày tải lên: 07/08/2014, 07:21

... of a cycle or a union of cycles of the permutation π : x → 2x of Z n (the map is a permutation since gcd(2,n) = 1). Only one cycle of D (and of π) has length 1, namely {0}.Foreachm-cycle C of ... family of all k-cycles by C k . For example, a 2-cycle consists of a pair of vertices and a pair of edges such that the pair of vertices is a subset of each edge. The above...

Ngày tải lên: 07/08/2014, 07:21

... referee for the useful remarks. the electronic journal of combinatorics 14 (2007), #N21 6 Regular spanning subgraphs of bipartite graphs of high minimum degree B´ela Csaba ∗† Submitted: Aug 1, 2007; ... 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...

Ngày tải lên: 07/08/2014, 15:22

... minimal r -twin-free graph for the induced subgraph relationship. Indeed, we have: the electronic journal of combinatorics 15 (2008), #N17 5 An r -twin-free graph contains a path P 2r+1 as an induced ... vertices in graphs, IEEE Transactions on Information Theory, vol 44, pp. 599-611, 1998. [6] A. Lobstein, Bibliography on identifying and locating-dominating codes in graphs, http://www...

Ngày tải lên: 07/08/2014, 15:22

... checking if the given graph is (d; ε 1 , ε 2 )-regular we need to consider only sets of the size ε 1 |V i |, i = 1, 2. In the following section we state our main results proved in Sections 3. In ... counting edges between sets U and W . Note, that each of these random variables has the same binomial distribution with expected value à = |U||W |d = 2 n 2 d. Applying Chernoff’s inequality...

Ngày tải lên: 07/08/2014, 15:23

... that any planar graph has a star coloring with k colors. While Corollary 4.2, Corollary 3.2, and [10] improve upon the upper bounds for planar graphs of high girth, less is known about planar graphs ... every planar graph of girth at least 5 can be star colored using 16 colors, every planar graph of girth at least 7 can be star colored with 9 colors, and planar graphs of...

Ngày tải lên: 07/08/2014, 21:20

... θ increases from 0 to π 2 . Also, the signs of these integrals alternate, so we can either throw out all of them or all but the first one, depending on whether the integral of h across R ⌊ r π ⌋ is positive ... establishes that the measurable chro matic number of the odd-distance graph is infinite. 4 Conclus i on and Open Problems The largest remaining question is whether or not...

Ngày tải lên: 07/08/2014, 21:21

... proof of Theorem 1, and discussed three different zeta functions of any graph. Various proofs of Bass’ theorem were known. Kotani and Sunada [15] proved Bass’ theorem by using the property of ... Ihara zeta function of a fractal graph, and gave a determinant expression of it. We define the Bartholdi zeta function of a fractal graph, and present its determinant expressi...

Ngày tải lên: 07/08/2014, 21:21

... graphs with maximum Laplacian spread among all tricyclic gr aphs of order n ≥ 11. Moreover, fo r 5 ≤ n ≤ 10, if G is one with maximum Laplacian spread of all tricyclic gra phs of order n, then G ... vertices of the star, respectively [4]. A tricyclic graph is a connected graph in which the number of edges equals the number of vertices plus two. In this paper, we stud...

Ngày tải lên: 07/08/2014, 21:21

... notion of universal cycles. In particular, we show that these cycles exist for certain classes of labeled graphs. In order to define a universal cycle of graphs, we must first extend the notion of ... Classification: 05C30 Abstract A universal cycle is a compact listing of a class of combinatorial objects. In this paper, we prove the existence of universal cycles of...

Ngày tải lên: 08/08/2014, 11:20

... fixed coloring χ of X, P (B c χ ) < 2 exp  − |Y | 8(8s) s  . Since there are at most s |X| colorings o f X, and since by Claim 1 |Y |  pn/2 and |X|  2p 2 n, the expected number of colorings ... journal of combinatorics 17 (2010), #R129 8 1.1 List coloring graphs The notion of list -coloring is a generalization of the notion of proper coloring, a nd has been studied extensively fo...

Ngày tải lên: 08/08/2014, 12:22