Incidence coloring of the squares of some graphs

The incidence chromatic number of G, denoted by χ_i(G), is the least number of colors such that G has an incidence coloring. In this paper, we determine the incidence chromatic number of the powers of paths, trees, which are min{n,2k+1}, and Δ(T²)+1, respectively. For the square of a Halin graph, we give an upper bound of its incidence chromatic number.     

Acyclic 5‐choosability of planar graphs without small cycles

A proper vertex coloring of a graph G = (V,E) is acyclic if G contains no bicolored cycle. A graph G is acyclically L‐list colorable if for a given list assignment L = {L(v): v: ∈ V}, there exists a proper acyclic coloring ? of G such that ?(v) ∈ L(v) for all v ∈ V. If G is acyclically L‐list colorable for any list assignment with |L (v)|≥ k for all v ∈ V, then G is acyclically k‐choosable. In this article, we prove that every planar graph G without 4‐ and 5‐cycles, or without 4‐ and 6‐cycles is acyclically 5‐choosable. © 2006 Wiley Periodicals, Inc. J Graph Theory 54: 245–260, 2007     

On the adjacent-vertex-strongly-distinguishing total coloring of graphs

For any vertex u∈V(G), let T_N(U)={u}∪{uv|uv∈E(G), v∈v(G)}∪{v∈v(G)|uv∈E(G)}and let f be a total k-coloring of G. The total-color neighbor of a vertex u of G is the color set C_f(u)={f(x)|x∈TN(U)}. For any two adjacent vertices x and y of V(G)such that C_f(x)≠C_f(y), we refer to f as a k-avsdt-coloring of G("avsdt"is the abbreviation of"adjacent-vertex-strongly- distinguishing total"). The avsdt-coloring number of G, denoted by X_(ast)(G), is the minimal number of colors required for a avsdt-coloring of G. In this paper, the avsdt-coloring numbers on some familiar graphs are studied, such as paths, cycles, complete graphs, complete bipartite graphs and so on. We proveΔ(G) 1≤X_(ast)(G)≤Δ(G) 2 for any tree or unique cycle graph G.     

Deterministic Models of the Simplest Chemical Reactions

We present a general mathematical framework for constructing deterministic models of simple chemical reactions. In such a model, an underlying dynamical system drives a process in which a particle undergoes a reaction (changes color) when it enters a certain subset (the catalytic site) of the phase space and (possibly) some other conditions are satisfied. The framework we suggest allows us to define the entropy of reaction precisely and does not rely, as was the case in previous studies, on a stochastic mechanism to generate additional entropy. Thus our approach provides a natural setting in which to derive macroscopic chemical reaction laws from microscopic deterministic dynamics without invoking any random mechanisms.     

最大度不小于5的外平面图的邻强边染色

图G(V,E)的一k-正常边染色叫做k-邻强边染色当且仅当对任意uv∈E(G)有,f[u]≠f[v],其中f[u]={f(uw)|uw∈E(G)},f(uw)表示边uw的染色.并且x'as(G)=min{k|存在k-图G的邻强边染色}叫做图G的图的邻强边色数.本文证明了对最大度不小于5的外平面图有△≤x'as(G)≤△ 1,且x'as(G)=△ 1当且仅当存在相邻的最大度点.     

混合超图的染色理论

混合超图是含有两种超边的超图，一种称为D-超边，一种称为C-超边，它们的区别主要体现在染色要求上．混合超图的染色，要求每-D-超边至少有两个点染不同的颜色，每一C-超边至少有两个点染相同的颜色．用颜色最多的染色所用的颜色数称为该混合超图的上色数，用颜色最少的染色所用的颜色数称为该混合超图的下色数．混合超图的染色理论是目前国际组合学界比较新的研究课题之一．本文主要概括介绍关于混合超图染色理论已经取得的一些成果，其中包含本文作者的研究成果．并提出了一些可供进一步研究的问题．     

树的Mycielski图的邻点可区别全色染色

A k-proper total coloring of G is called adjacent distinguishing if for any two adjacent vertices have different color sets.According to the property of trees,the adjacent vertex distinguishing total chromatic number will be determined for the Mycielski graphs of trees using the method of induction.     

On the Acyclic Chromatic Number of Hamming Graphs

An acyclic coloring of a graph G is a proper coloring of the vertex set of G such that G contains no bichromatic cycles. The acyclic chromatic number of a graph G is the minimum number k such that G has an acyclic coloring with k colors. In this paper, acyclic colorings of Hamming graphs, products of complete graphs, are considered. Upper and lower bounds on the acyclic chromatic number of Hamming graphs are given. Gretchen L. Matthews: The work of this author is supported by NSA H-98230-06-1-0008.     

Linear colorings of simplicial complexes and collapsing

A vertex coloring of a simplicial complex Δ is called a linear coloring if it satisfies the property that for every pair of facets (F₁,F₂) of Δ, there exists no pair of vertices (v₁,v₂) with the same color such that v₁∈F₁?F₂ and v₂∈F₂?F₁. The linear chromatic numberlchr(Δ) of Δ is defined as the minimum integer k such that Δ has a linear coloring with k colors. We show that if Δ is a simplicial complex with lchr(Δ)=k, then it has a subcomplex Δ^′ with k vertices such that Δ is simple homotopy equivalent to Δ^′. As a corollary, we obtain that lchr(Δ)?Homdim(Δ)+2. We also show in the case of linearly colored simplicial complexes, the usual assignment of a simplicial complex to a multicomplex has an inverse. Finally, we show that the chromatic number of a simple graph is bounded from above by the linear chromatic number of its neighborhood complex.     

一些图的邻点可区别关联着色

在图的关联着色概念的基础上定义了图的邻点可区别关联着色及邻点可区别关联色数,研究了圈、完全二部图、Cm.Fn图的邻点可区别关联着色,并确定了它们的邻点可区别关联色数.