Báo cáo toán học: "Partitioning 3-colored complete graphs into three monochromatic cycles" ppsx

... of A 3 the electronic journal of combinatorics 18 (2011), #P53 6 Partitioning 3-colored complete graphs into three monochromatic cycles ∗ Andr´as Gy´arf´as, Mikl´os Ruszink´o Computer and Automation ... vertices can be partitioned into three monochromatic cycles. From this, using our earlier results, actually it follows that we can partition all the ver tices into at most...

Ngày tải lên: 08/08/2014, 14:22

... led to this work. References [1] N. Alon, S. Hoory, N. Linial, The Moore bound for irregular graphs, Graphs and Combinatorics 18 (2002), 53–57. [2] N. Biggs, Algebraic Graph Theory, Cambridge University ... series of dense graphs of high girth, Bull. Amer. Math. Soc. 32 (1995), 73–79. [9] F. Lazebnik, V. A. Ustimenko and A. J. Woldar, Properties of Certain Families of 2k–Cycle Free Grap...

Ngày tải lên: 07/08/2014, 08:22

... Partitioning complete multipartite graphs by monochromatic trees, J. Graph Theory 48 (2005), 133-141. [6] M. Kano and X. Li, Monochromatic and heterochromatic subgraphs in edge-colored graphs - a ... Partitioning by monochromatic trees, J. Combin. Theory. Ser. B 68 (1996), 218-222. [4] Z.M. Jin, M. Kano, X. Li and B. Wei, Partitioning 2-edge-colored complete multipar- tite grap...

Ngày tải lên: 07/08/2014, 21:20

... point set which is a complete lattice. Moreover, the common fixed point set Fix ( T ) is a complete lattice. Proof.Let T 0 ∈ T be the map for wh ich Fix(T 0 )=X 0 is a nonempty complete lattice. Since ... we characterize the externally complete subsets of trees. Theorem 2.1. Let X be a tree. A subset M of X is externally complete if and only if M is convex, Dedekind complete, and a...

Ngày tải lên: 20/06/2014, 21:20

... 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. ... an involution and {e, σ n 2 } is the center of D n . The non-trivial subgroups of D n fall into one of three types: a subgroup of <σ>, the cyclic half of D n , a subgroup isomorph...

Ngày tải lên: 07/08/2014, 06:20

... 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 from P have ... 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...

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

... classes of shriekless graphs correspond to integer partitions. Proposition 3.5. Shriekless graphs not containing K − 5 correspond to integer par- titions which either have three or fewer parts ... complement of such a graph either has no edges or consists of the the disjoint union of three or fewer complete graphs. Proof. The complement of K − 5 is a graph on five vertices with onl...

Ngày tải lên: 07/08/2014, 06:20

... generality, α ≥ n/ log n.Letq =(1/2) log n/α n. Before coloring, randomly partition the n vertices into n/q blocks, each of size q, ignoring the remainder. Greedily color the vertices of each block ... uncertainty is which x out of k/2 block-vertices are being presented in each round. We shall describe three strategies for Alice that force Bob to use many colors. A strategy involves spe...

Ngày tải lên: 07/08/2014, 06:20