Báo cáo toán học: "Graph Minors and Minimum Degree" pps

... 19 v ∈ C 5 and w ∈ K 3 . Observe that vw is in two triangles vwx and vwy, where x and y are the neighbours of v in C 5 . Since both x and y have degree 4 in G/vw, some edge incident to x and some ... common neighbour of r and r  . Let B  be the set of blue edges with respect to r  . Now B and B  (as well as R and R  ) differ only in rx and r  x. Since (5) only considers...

Ngày tải lên: 08/08/2014, 12:23

... w, x} and edge set {uv, vw, wx} such that u and x have the sa me color. Consider two vertices (uv) s and (xw) s . It was shown that colors of (uv) s and (xw) s should be the same as u and x, ... Graph homomorphims through random walks, J. Graph Theory, 44 (2003) , 15–38. [5] A. Daneshgar and H. Hajia bolhassan, Graph homomorphisms and nodal domains, Linear Algebra and its Appl...

Ngày tải lên: 08/08/2014, 11:20

... manner proceed if a = c and b = d. ✷ 3 New solutions to the classic Obe r wolfach Problem Our constructions are presented in Theorems 3.4, 4.1 and 4.2 and need some machinery and preliminary lemmas ... integer and let t 1 , . . . , t 2s , k 1 , . . . , k 2s and d be positive integers such that t j ≥ 3 and t j k j = 3d, for every j = 1, . . . , 2s. If each t j = 3 whenever d =...

Ngày tải lên: 08/08/2014, 14:22

Ngày tải lên: 05/08/2014, 09:46

Ngày tải lên: 05/08/2014, 15:21

... i minimum, and u j /∈ X with j maximum. Here, u i = a 0 = u j . Because of equalities (1) and (2), we may apply Fact 2. Parts (a) and (b) imply that {u 1 , ,u i } is a clique, and parts (a) and ... x i is adjacent to both a j and a j+1 .FormS from T by inserting x i between a j and a j+1 , i.e., remove the edges x i S(x i )anda j a j+1 , and add the edges x i a j and x i a...

Ngày tải lên: 07/08/2014, 06:22

... ···,v s and w is adjacent to w 1 , ···,w s . Suppose each vertex in G[P ] is precolored with its subscript. G is planar and so does not contract to K 5 ,ands +3 colors are both necessary and sufficient ... Albertson and Joan P. Hutchinson, Hadwiger’s conjecture and six- chromatic toroidal graphs, in: Graph Theory and Related Topics, Academic Press, New York, 1979, 35-40. [4] Michael...

Ngày tải lên: 07/08/2014, 07:21

... K r minor, and this completes the proof. The relation between α 2k and α 2k+1 in Corollary 1.6 cannot be extended to α 2k+1 and α 2k+2 as shown by the following examples (which are all planar and hence ... ≤ i<j≤ q) and two of their paths P i a and P j b where a = b. Suppose that they intersect in a vertex v.Denotebyx =dist G (v i ,v), y =dist G (v, A a ), z =dist G (v j ,v),...

Ngày tải lên: 07/08/2014, 07:21

... one-factorizations F = {F 0 , ,F 2n−2 } and G = {G 0 , ,G 2m−2 } of K 2n and K 2m on the points X and Y , respectively, it is easy to see that FG =  F i G j : i =0, ,2n − 2andj =0, ,2m − 2    F ∗ i : ... equal to 1, so f =1andd = e.This contradicts the assumption that d>e. Therefore k> and the right side of (1) is even. Now, suppose that f isodd. Thentheleftsideof(1)isodd,and...

Ngày tải lên: 07/08/2014, 08:22

... G[X] and G[X] are critical, 2-connected and non-bipartite, and that |F ∩ EG[X]| ≡ |X| − 1 2 (mod 2) for all 1-factors F . Then the unique brick resulting from the decomposition of G into bricks and ... passes through x. Let e and f be the edges of C incident on x. Let u and v, respectively, be the ends of these edges in X. Let M e and M f be perfect matchings of G containing e...

Ngày tải lên: 07/08/2014, 15:22