Báo cáo toán học: "Coloring with no 2-colored P4’s" pdf

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Ngày tải lên: 05/08/2014, 15:20

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Ngày tải lên: 05/08/2014, 15:21

... question in contact geometry, i.e., closed submanifolds with equal Wirtinger angles and parallel mean curvature vector fields, immersed into a Sasakian space form, and obtain the following: Theorem ... 149–160 Submanifolds with Parallel Mean Curvature Vector Fields and Equal Wirtinger Angles in Sasakian Space Forms * Guanghan Li School of Mat...

Ngày tải lên: 06/08/2014, 05:20

... augment the automaton with green and amber plates, a dictionary, and a notepad. The dictionary contains a chosen representative of each equivalence class of rise-fall sequences. Metaphor- ically, the ... natural to associate with a data structure the collection of such permutations which it can realize. Furthermore, most natural data structures have a hereditary property. That i...

Ngày tải lên: 07/08/2014, 07:21

... absence of each character, is distinct. Note that (2/3 − d ) d ≤ C (d) 1 ≤ (2 +  d ) d , for some  d → 0. 3 Strings with maximally many distinct substrings We close with a solution to a simpler ... string, but for d = 2 no such infinite string exists. 2 Strings with maximally many distinct subsequences Let Σ be a finite alphabet of size d; without loss of generality we t...

Ngày tải lên: 07/08/2014, 08:20

... and w with the same color. Now the vertex v between u, w on P 4 is not in C, but since u, w areatdistanceatleast3onC the path uvw together with one of the u, w-segments of C yields a shorter non-contractible ... preliminaries Suppose F is a nonempty family of connected bipartite graphs, each with at least 3 vertices. An r-coloring of a graph G is said to be F-free if G contains no 2-...

Ngày tải lên: 07/08/2014, 08:20

... continuity that the chromatic polynomial has a root in the interval (1, 2). We can perform a similar analysis on the graphs obtained by adding the single edge v 1 v 4 to X(s, t) with the following ... an in nite family of 3-connected non-bipartite graphs with chromatic roots in the interval (1, 2) thus resolving a conjecture of Jackson’s in the negat...

Ngày tải lên: 07/08/2014, 13:21

... most graphs on n vertices contain substantially many copies of any fixed graph, but contain no complete bipartite subgraphs with both parts larger than C log n, for some C > 0, independent of n. Hence, ... graph of order 2; - K 2 (s, t) for the complete bipartite graph with parts of size s and t; - f| X for the restriction of a map f to a set X. Specific notation Suppos...

Ngày tải lên: 07/08/2014, 15:23

... first. If y does not begin with a then replace it with one of its conjugates that does. Then each occurrence of the letter b is preceded by a: we can replace such a pair with φ(a). Similarly each ... replaced with φ(c). The remaining occurrences of a can be replaced with φ(a) and we see that y is in the range of φ. Suppose the factors of y come from the fourth set. If y does not begi...

Ngày tải lên: 07/08/2014, 21:20

... of finding connected graphs of maximal spectral radius with given number of vertices and edges (but arbitrary degree sequences). Brualdi and Solheid [4] have shown that such graphs have stepwise ... of those graphs that have largest spectral radius in the class of all connected graphs with a given degree sequence. We show that in such a graph the degree sequen...

Ngày tải lên: 07/08/2014, 21:20

... follows that H u,π 2 (q) = P u,w (q) + q h 2 E u (q) . Since H u,π 2 (q) − P u,w (q) has nonnegative coefficients and deg P u,w (q) ≤ (h − 1) /2 < h − 1, P u,w (q) = 1 + · · · + q s 1 4 For tho se readers ... w]: I:  (y + 1) z · · · 1( y + z + 2) · · · (y + 2), (y + z + 2)(y + 1) y · · · 2(y + z + 1)...

Ngày tải lên: 08/08/2014, 01:20

... words. 1 Words with intervening neighbours Let G be the Coxeter graph of a Coxeter group with generators S. Consider a word w in the alphabet S. Definition 1.1. A word has the intervening neighbours property ... groups. the electronic journal of combinatorics 17 (2010), #N9 3 Words with intervening neighbours in infinite Coxeter groups are reduced Henrik Eri...

Ngày tải lên: 08/08/2014, 01:20

... with exactly one descending vertex also has exa ctly one ascending vertex. Also, conditions (i) and (iii) do not change b ecause they have nothing to do with whether a block is ascending or descending. ... same block, and if that block is ascending then v and v ′ are in the same order as their successors, whereas if it is descending they are in the opposite order. Now sup...

Ngày tải lên: 08/08/2014, 11:20

... could be several conical subsets that are large. Fortunately, we have the following Lemma 3 Let S be an arc with a conical subset T with excess e. Then the excess e ′ of any other conical subset ... (q + 5)/2 can contain at most one conical subset with excess a t most 2. Proof : Assume S has a conical subset T with excess e  2. Then by Lemma 3, a ny other conical subset...

Ngày tải lên: 08/08/2014, 12:22

... research in random graph theory is the component structure of the random graph G n,m (a graph drawn uniformly at random from all graphs ∗ A preliminary version of this paper appeared in the proceedings ... into an initially empty graph. Then the theorem states that a. a.s. a linear-sized giant component’ emerges quite precisely at the point where the avera...

Ngày tải lên: 08/08/2014, 12:22