Báo cáo toán học: "Sum List Coloring 2 × n Arrays" pot

... t 2 ≥ 2n/ 3. Finally we see that the size of f is n( n +1) /2+ t 1 + n( n +1) /2+ t 2 ≥ n( n +1)+ 2n/ 3 = n 2 +  5n/ 3. ✷ the electronic journal of combinatorics 9 (20 02) , #N8 3 Now we try another coloring ... t 1 + (n − 2t 1 ) =n − t 1 and t 1 + t 2 ≥ 2t 1 . Suppose t 1 + t 2 < 2n/ 3. Then 2n/ 3 > ;n t 1 (so t 1 > ;n/ 3) and 2t 1 < 2n/ 3 which yields the...

Ngày tải lên: 07/08/2014, 06:23

... . Then {•, •, . . . , • α : α ∈ (0, 1)} is an ascending family of n- norms on X. We call these n- norms as α -n- norms on X corresponding to the fuzzy n- norm on X. Definition 2. 3 Let X be any non-empty ... space. Remark 3.1 In a 2- fuzzy n- normed linear space (X, N) , N( f 1 , f 2 , . . . , f n , ·) is a non-decreasing function of R for all f 1 , f 2 , . . . , f n ∈  (X)....

Ngày tải lên: 20/06/2014, 21:20

... decomposition to include all infinite 2- connected graphs. 1 Introduction In [5], Tutte presents a decomposition of a finite 2- connected graph into 3-connected graphs, cycles and bonds. This is useful in ... University of Toronto Press, Toronto, Ont.; Oxford University Press, London 1966 the electronic journal of combinatorics 11 (20 04), #R25 10 Decomposing infinite 2- connected graphs into...

Ngày tải lên: 07/08/2014, 08:20

... + n is even and j(2j − 1) ≤ n. 4 Congruences Berkovich and Garvan’s motivation for introducing the BG-rank lay in their wish to refine some known congruences for p (n) . We can give quite elementary ... restriction that the result of the deletion the electronic journal of combinatorics 13 (20 06), #N1 8 2 References [1] Alexander Berkovich and Frank Garvan, On the Andrews-Stanley refineme...

Ngày tải lên: 07/08/2014, 13:21

... D is even then G even-contains 2A or 2B since C is odd. Otherwise G is of type G 2 . Concerning statement (3), if E(G) is an even circuit or G is isomorphic to K 2 , then G is alternating-realizable. ... 2- connected graph G[E(H) ∪ P ] by an ear addition. Note that K contains the odd circuit A not containing e. By Lemma 1 there exists an even circuit C in K containing e. But by the defini...

Ngày tải lên: 07/08/2014, 13:21

... a winning strategy in the A-game on G 1 with k colours and she also has a winning strategy with k colours in the B-game on G 2 then she can obtain a winning strategy on G in the following way: ... be a 2 -list- assignment of C 4 , other than the lists in Figure 4 and Fig- ure 5. Then Alice has a winning strategy in the B-game list colouring on (C 4 , L). Proof. Let V (C 4 ) = {x 1 , x...

Ngày tải lên: 07/08/2014, 15:22

... Since H 1 is 2- connected and since F i has an edge connecting it to F i−1 and another edge connecting it to F i+1 , the graph G k is 2- connected. ✷ the electronic journal of combinatorics 15 (20 08), ... dominating set D must contain 12 vertices in V (H 2 ∪H  2 )−x 1 −y l , and by (P2) D must contain 16 vertices in each V (F j ). This completes our proof. ✷ the electronic journal of...

Ngày tải lên: 07/08/2014, 15:22

... T − y,x 2 T − z,x 3 z (b) T − y,x 2 T − x 2 y,x 14. C 2 × C 2 × C 2 × C 2 = x, y, z, w : x 2 = y 2 = z 2 = w 2 = 1. (a) ˆ D = (T − x,y )(T − w,z ) the electronic journal of combinatorics 15 (20 08), ... be written as D =  h∈H a h h where a h ∈ {0, 1, 2} . Note that a h = |D ∩ {h, hz}| for h ∈ H. Since  h∈H a h = 2m 2 − m and  h∈H a 2 h = m 2 + 2(...

Ngày tải lên: 07/08/2014, 21:20

... component of G 1 and a vertex for each component of G 2 . For each vertex of G, place an edge in H joining the vertices representing the components containing it in G 1 and G 2 (H is the “intersection graph” ... that 1. n i = 15 (2 i ) − 6 and R i is connected, 2. R i decomposes into a 2- factor on R  i and n i /3 disjoint triangles, and 3. α(R  i ) = 4 (2 i ) − 2, with a maxim...

Ngày tải lên: 07/08/2014, 21:21

... zu senken, und zwar für natürlich vorkommende Substanzen auf Konzentrationen nahe den natürlichen Hintergrundkonzentrationen und für synthetische Chemikalien auf Konzentrationen nahe Null. ... Berechnung kann man Daten aus einem unbelasteten Referenzgebiet verwenden und den Mittelwert der Konzentrationen als BC definieren. Zur Unterscheidung von Werten, die als Hintergrundbelastung ange...

Ngày tải lên: 20/06/2014, 20:20