Báo cáo toán học: "Online Coloring Known Graphs" docx

... 68W25. Keywords: graph coloring, online algorithms. Abstract The problem of online coloring an unknown graph is known to be hard. Here we consider the problem of online coloring in the relaxed ... independence number α are known in advance. The unknown case can be handled via a doubling technique, see [5]. Without loss of generality, α ≥ n/ log n.Letq =(1/2) log n/α n. Before colori...

Ngày tải lên: 07/08/2014, 06:20

Ngày tải lên: 07/08/2014, 06:20

... permutation w e ∈ S p by reading the labels of the internal nodes from left to right. It is well known (see for example [LR, Prop osition 2.3]) that as T varies over T p and e varies over E(T )

Ngày tải lên: 08/08/2014, 12:22

... 2-colored. Every star coloring is an acyclic coloring but star coloring a graph typically requires more colors than acyclically coloring the same graph. In general, many star coloring questions ... such that G has a k-star coloring is the star chromatic number of G. In 1973 Gr¨unbaum [5] introduced star colorings and acyclic colorings. An acyclic col- oring is a proper coloring...

Ngày tải lên: 07/08/2014, 21:20

Ngày tải lên: 07/08/2014, 06:20

... corresponds with the labeling l  from the introduction. We claim that this is a 2-distinguishing coloring of O u , i.e. that the electronic journal of combinatorics 3 (1996), #R18 6 such that ψ(vg)=ψ(v) ... ≤ i ≤ s,henceσ dj fixes all of G. This contradicts our assumption that G realizes D n . Thus our coloring 2-distinguishes G. ✷ Theorem 6 D(D n )={2} unless n =3, 4, 5, 6, 10, in which...

Ngày tải lên: 07/08/2014, 06:20

... theorem applied to the red-blue coloring of 2-element subsets of a large independent set. Given a Ramseyan class of graphs P we ... let x and y be a pair of non-adjacent distinct vertices of GP. For every graph consider a fixed coloring of all pairs {x, y} of nonadjacent vertices - we color e = {x, y} blue if G + {e} belongs

Ngày tải lên: 07/08/2014, 06:20

... the first coloring, receive distinct colors in the second coloring. For a survey of the results on orthogonal edge colorings the reader is referred to [1]. The results on orthogonal edge coloring ... <n,wemusthavex> √ n . 4 Strong orthogonal colorings A k-strong orthogonal coloring, is a k-orthogonal coloring c 1 , ,c k ,whereforeachvertex v and for every pair of distinct colori...

Ngày tải lên: 07/08/2014, 06:20

... published in 1989 [7]. It appears that this paper is not well -known, although it contains results for g =13,14, 15, 16 which are still the best known in 1998. Recently there has been some more progress ... of c is known to lie between 0.5 and 0.75. At the end of the paper there is a selection of open questions, several of them containing suggestions which might lead to improvements in th...

Ngày tải lên: 07/08/2014, 06:22

... a 2 ≤···≤a k . We shall show that θ(a 1 ,a 2 , ···,a k )isχ-unique if a k <a 1 + a 2 . It is well known (see [8]) that Lemma 5.2 If G ∼ H, then g(G)=g(H). ✷ Theorem 5.1 If 2 ≤ a 1 ≤ a 2 ≤···≤a k <a 1 + ... shall solve this problem under the condition that max 1≤i≤k a i ≤ min 1≤i<j≤k (a i + a j ). 2 Known results For two non-empty graphs G and H,anedge-gluing of G and H is a graph...

Ngày tải lên: 07/08/2014, 08:20