The circular chromatic number of a graph is an important parameter of a graph. The distance graph G(Z,D) , with a distance set D , is the infinite graph with vertex set Z={0,±1,±2,...} in which tw...The circular chromatic number of a graph is an important parameter of a graph. The distance graph G(Z,D) , with a distance set D , is the infinite graph with vertex set Z={0,±1,±2,...} in which two vertices x and y are adjacent iff y-x∈D . This paper determines the circular chromatic numbers of two classes of distance graphs G(Z,D m,k,k+1 ) and G(Z,D m,k,k+1,k+2 ).展开更多
A graph is called star extremal if its fractional chromatic number is equal to its circular chromatic number. We first give a necessary and sufficient condition for a graph G to have circular chromatic number V(G)/α(...A graph is called star extremal if its fractional chromatic number is equal to its circular chromatic number. We first give a necessary and sufficient condition for a graph G to have circular chromatic number V(G)/α(G) (where V(G) is the vertex number of G and α(G) is its independence number). From this result, we get a necessary and sufficient condition for a vertex-transitive graph to be star extremal as well as a necessary and sufficient condition for a circulant graph to be star extremal. Using these conditions, we obtain several classes of star extremal graphs.展开更多
The circular chromatic number and the fractional chromatic number are two generalizations of the ordinary chromatic number of a graph. We say a graph G is star extremal if its circular chromatic number is equal to its...The circular chromatic number and the fractional chromatic number are two generalizations of the ordinary chromatic number of a graph. We say a graph G is star extremal if its circular chromatic number is equal to its fractional chromatic number. This paper gives an improvement of a theorem. And we show that several classes of circulant graphs are star extremal.展开更多
The circular chromatic number and the fractional chromatic number are two generalizations of the ordinary chromatic number of a graph. A graph is called star extremal if its fractional chromatic number equals to its c...The circular chromatic number and the fractional chromatic number are two generalizations of the ordinary chromatic number of a graph. A graph is called star extremal if its fractional chromatic number equals to its circular chromatic number (also known as the star chromatic number). This paper studies the star extremality of the circulant graphs whose generating sets are of the form {±1,±k} .展开更多
Abstract. Let G be a graph with edge set E(G). S E(G) is called an edge cover of G ifevery vertex of G is an end vertex of some edges in S. The edge covering chromatic numberof a graph G, denoted by Xc(G) is the maxim...Abstract. Let G be a graph with edge set E(G). S E(G) is called an edge cover of G ifevery vertex of G is an end vertex of some edges in S. The edge covering chromatic numberof a graph G, denoted by Xc(G) is the maximum size of a partition of E(G) into edgecovers of G. It is known that for any graph G with minimum degree δ,δ- 1 The fractional edge covering chromatic number of a graph G, denoted by Xcf(G), is thefractional matching number of the edge covering hypergraph H of G whose vertices arethe edges of G and whose hyperedges the edge covers of G. In this paper, we studythe relation between X’c(G) and δ for any graph G, and give a new simple proof of theinequalities δ - 1 ≤ X’c(G) ≤ δ by the technique of graph coloring. For any graph G, wegive an exact formula of X’cf(G), that is,where A(G)=minand the minimum is taken over all noempty subsets S of V(G) and C[S] is the set of edgesthat have at least one end in S.展开更多
文摘The circular chromatic number of a graph is an important parameter of a graph. The distance graph G(Z,D) , with a distance set D , is the infinite graph with vertex set Z={0,±1,±2,...} in which two vertices x and y are adjacent iff y-x∈D . This paper determines the circular chromatic numbers of two classes of distance graphs G(Z,D m,k,k+1 ) and G(Z,D m,k,k+1,k+2 ).
文摘A graph is called star extremal if its fractional chromatic number is equal to its circular chromatic number. We first give a necessary and sufficient condition for a graph G to have circular chromatic number V(G)/α(G) (where V(G) is the vertex number of G and α(G) is its independence number). From this result, we get a necessary and sufficient condition for a vertex-transitive graph to be star extremal as well as a necessary and sufficient condition for a circulant graph to be star extremal. Using these conditions, we obtain several classes of star extremal graphs.
文摘The circular chromatic number and the fractional chromatic number are two generalizations of the ordinary chromatic number of a graph. We say a graph G is star extremal if its circular chromatic number is equal to its fractional chromatic number. This paper gives an improvement of a theorem. And we show that several classes of circulant graphs are star extremal.
文摘The circular chromatic number and the fractional chromatic number are two generalizations of the ordinary chromatic number of a graph. A graph is called star extremal if its fractional chromatic number equals to its circular chromatic number (also known as the star chromatic number). This paper studies the star extremality of the circulant graphs whose generating sets are of the form {±1,±k} .
基金the National Natural Science Foundation the Doctoral Foundation of the Education Committee of China.
文摘Abstract. Let G be a graph with edge set E(G). S E(G) is called an edge cover of G ifevery vertex of G is an end vertex of some edges in S. The edge covering chromatic numberof a graph G, denoted by Xc(G) is the maximum size of a partition of E(G) into edgecovers of G. It is known that for any graph G with minimum degree δ,δ- 1 The fractional edge covering chromatic number of a graph G, denoted by Xcf(G), is thefractional matching number of the edge covering hypergraph H of G whose vertices arethe edges of G and whose hyperedges the edge covers of G. In this paper, we studythe relation between X’c(G) and δ for any graph G, and give a new simple proof of theinequalities δ - 1 ≤ X’c(G) ≤ δ by the technique of graph coloring. For any graph G, wegive an exact formula of X’cf(G), that is,where A(G)=minand the minimum is taken over all noempty subsets S of V(G) and C[S] is the set of edgesthat have at least one end in S.
