Báo cáo toán học: "Decomposing complete equipartite graphs into short odd cycle" ppt

... of complete equipartite graphs: 3 and 5 parts, Discrete Math. 310 (20 10), 241–254. [3] E. J. Billington, N. J. Cavenagh and B. R. Smith, Path and cycle decompositions of complete equipartite graphs: ... an edge-disjoint decomposition of a complete graph K n (n odd) into k- cycles was finally completed in [1] and [11]. This graph can be regarded as a complete equipartite gra...

Ngày tải lên: 08/08/2014, 12:22

... of length at most 2k, each cycle in the vine has odd length. Now suppose P is another uv-geodesic. Then P i ⊂ P for some i.SinceP i ∪P ∗ i is an odd cycle, we may assume |P i | < |P ∗ i |. By ... electronic journal of combinatorics 12 (2005), #N5 4 the analogous extremal problem when some of the short odd cycles are forbidden seems to be very difficult. For example, it is known that...

Ngày tải lên: 07/08/2014, 08:22

... the grammar to simple graphs in Section 5.4). In the case of a class of graphs, we will need to take both vertices and edges into account. Accordingly, we consider a class of graphs as a species ... candidates make it possible to completely decompose a 2- connected graph into 3-connected components. We consider here only 2-connected graphs with at least 3 edges (graphs with less e...

Ngày tải lên: 07/08/2014, 21:21

... Szegedy, Efficient testing of large graphs, Proceedings of the 40 th IEEE FOCS (1999), to appear. [2] N. Alon and R. Yuster, Almost H-factors in dense graphs, Graphs and Combi- natorics 8 (1992), ... copies of K(h, a), the complete h-partite graph with a vertices in each color class. In [1] a variant of the Regularity Lemma which is suitable for dealing with in- duced subgraphs in very ge...

Ngày tải lên: 07/08/2014, 06:20

... 2-connected finite graph into 3-connected graphs, cycles and bonds. This decomposition has been used to reduce problems on 2-connected graphs to problems on 3-connected graphs. Motivated by a problem ... planar graphs, we generalize Tutte’s decomposition to include all infinite 2-connected graphs. 1 Introduction In [5], Tutte presents a decomposition of a finite 2-connected graph into...

Ngày tải lên: 07/08/2014, 08:20

Ngày tải lên: 05/08/2014, 15:21

... minimal graphs for match- ings,inThe Theory and Applications of Graphs (G.Chartrand, ed.) Wiley (1981) pp.159–168. [5] S.A.Burr, P.Erd˝os, R.J.Faudree, C.C.Rousseau and R.H.Schelp, Ramsey minimal graphs ... infinite number of graphs J such that J → (F, G)butifwedeletefromJ any edge e the graph J − e obtained in this way does not have this property. Introduction. All graphs in this no...

Ngày tải lên: 07/08/2014, 06:20

... possible orbits and providing 2-distinguishing colorings for graphs with 6-orbits, and graphs without 6-orbits, but with 3-orbits. Clearly graphs with largest orbit size 2 can be 2-distinguished. ... are all pairwise relatively prime. The bipartite graphs formed by the vertices of two orbits and the edges between the orbits are then either complete or empty. By Lemma 5 below, D n is...

Ngày tải lên: 07/08/2014, 06:20

... Examples of critical P (r, b) graphs are disjoint unions of b − 1 copies of of complete k-partite graphs in which every part has r − 1 vertices. Other critical graphs can be obtained by adding ... a property P of graphs will be called Ramseyan if large graphs from P contain large monochromatic subgraphs. It is easy to see that P is Ramseyan if and only if large enough graphs fro...

Ngày tải lên: 07/08/2014, 06:20

... and planar graphs are 5- degenerate. Obviously, d-degenerate graphs have a greedy coloring with d +1colors. The next theorem bounds the k-orthogonal chromatic number of d-degenerate graphs. Theorem ... the chromatic number. We also study the structure of graphs having an optimal or perfect orthogonal coloring, and show that several classes of graphs always have an optimal or perfect...

Ngày tải lên: 07/08/2014, 06:20