Báo cáo toán học: "A note on graph coloring extensions and list-colorings" pptx

... A note on graph coloring extensions and list-colorings Maria Axenovich Department of Mathematics Iowa State University, ... Albertson posed the following question. Take a graph described above, precolor a fixed set of vertices P in ∆ colors arbitrarily. Under what condition on P can we extend that coloring to a proper coloring ... We need a couple of definitions first. A bloc...

Ngày tải lên: 07/08/2014, 07:21

... Split graph, Burkar d–Hammer c ondition, Burkard–Hammer graph, hamil- tonian graph, maximal nonhamiltonian split graph. 1. Introduction All graphs considered in this paper are finite undirected graphs ... Theory of Graphs, Allyn and Bacon, Boston, 1971. Note on Maximal Nonhamiltonian Burkard–Hammer Graphs 399 exists a maximal nonhamiltonian Burkard–Hammer graph G = S(I ∪ K, E) wit...

Ngày tải lên: 06/08/2014, 05:20

... Orientations and Edge Functions on Graphs, in: A.D.Keedwell (ed.), Surveys in Combinatorics, London Math. Soc. Lecture Notes 66, 1991, 161–185. [9] J. Neˇsetˇril and V. R¨odl, On a Probabilistic Graph- Theoretical ... a constant κ<2/3, then it outputs a cover graph whp. Note that the output graph will have whp girth equal to 4. On a related note we point to [8] which sur...

Ngày tải lên: 07/08/2014, 06:20

... irregular graphs, Graphs and Combinatorics 18 (2002), 53–57. [2] N. Biggs, Algebraic Graph Theory, Cambridge University Press, Cambridge, second edition, 1993. [3] J.A. Bondy, M. Simonovits, Cycles ... lower bound on the number of non-returning walks, by Alon, Hoory and Linial [1], which gives the best known upper bound on ex(n, {C 3 ,C 4 , ,C 2k }): Proposition 6 Let G be an n-vert...

Ngày tải lên: 07/08/2014, 08:22

... be denoted by R P .From all possible 3-colorings of a random graph, only its rigid colorings are used in order to obtain a smaller expression for the right-hand side in (1). If by R  we denote ... (3) When conditioning on the event C P 0 , the random graphs of the resulting probability space may contain edges only from within the edges that connect vertices of different partitions of P 0 ....

Ngày tải lên: 07/08/2014, 06:20

... denotes the collection of automorphisms of the graph G andiddenotes the identity map. One says that such a coloring “destroys the symmetries” of G. Every graph G is then |G|-distinguishable and ... L ∈ Σ P k .Above, the notation · , · refers to some canonical pairing function. With these definitions, NP = Σ P 1 ,coNP=Π P 1 ,andtheclassesΣ P k and Π P k form a neat hierarchy contain...

Ngày tải lên: 07/08/2014, 06:22

... A note on odd cycle-complete graph Ramsey numbers Benny Sudakov ∗ Department of Mathematics, Princeton University, Princeton, NJ 08544, USA and Institute for Advanced Study, Princeton, NJ ... result. References [1] M. Ajtai, J. Koml´os and E. Szemer´edi, A note on Ramsey numbers, J. Combinatorial Theory A 29 (1980), 354-360. [2] N. Alon, M. Krivelevich and B. Sudakov, Colorin...

Ngày tải lên: 07/08/2014, 06:23

... com- ments. References [1] Andrew Berget, Andrew Manion, Molly Maxwell, Aaron Potechin, and Victor Reiner. The critical group of a line graph. arxiv:math.CO/0904.1246. [2] Alexander E. Holroyd, Lionel Levine, ... Propp, and David B. Wilson. Chip-firing and rotor-routing on directed graphs. In In and out of equilibrium. 2, volume 6 0 of Progr. Probab., pages 331–364. Birkh¨auser, Bas...

Ngày tải lên: 08/08/2014, 14:23

... factorial i f and only if G is a non-trivial induced subgraph of P 4 . From now on, we assume that none of the forbidden graphs is an induced subgraph of P 4 . This leaves us with 12 non-trivial graphs ... section we introduce basic notations. In Section 2, we verify the conjecture for all factorial classes defined by forbidden induced subgraphs on at most 4 vertices with one exception. T...

Ngày tải lên: 08/08/2014, 14:23

... H ¨ ormann [8], Wu [9, 10], and Ye and Wu [11]. Huang and Zhang [12] and Zhang and Yang [13] obtained ASCLT results for self-normalized version. Under mild moment conditions ASCLT follows from the ... Foundation of China (11061012), the project supported by program to Sponsor Teams for Innovation in the Construction of Talent Highlands in Guangxi Institutions of Higher Learning ([20...

Ngày tải lên: 20/06/2014, 21:20