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
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
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
In this paper, we will explain the relevance of the starant graphs, graphs created by us in the year of 2002. They were basically circulant graphs with a star graph that connects to all the vertices of the circulant g...In this paper, we will explain the relevance of the starant graphs, graphs created by us in the year of 2002. They were basically circulant graphs with a star graph that connects to all the vertices of the circulant graphs from inside of them, but they did not exist as a separate object of study in the year of 2002, as for all we knew. We now know that they can be used to model even social networking interactions, and they do that job better than any other graph we could be trying to use there. With the development of our mathematical tools, lots of conclusions will be made much more believable and therefore will become much more likely to get support from the relevant industries when attached to new queries.展开更多
Let F={H_(1),...,H_(k)}(k≥1)be a family of graphs.The Tur´an number of the family F is the maximum number of edges in an n-vertex{H_(1),...,H_(k)}-free graph,denoted by ex(n,F)or ex(n,{H_(1),H_(2),...,H_(k)}).Th...Let F={H_(1),...,H_(k)}(k≥1)be a family of graphs.The Tur´an number of the family F is the maximum number of edges in an n-vertex{H_(1),...,H_(k)}-free graph,denoted by ex(n,F)or ex(n,{H_(1),H_(2),...,H_(k)}).The blow-up of a graph H is the graph obtained from H by replacing each edge in H by a clique of the same size where the new vertices of the cliques are all different.In this paper we determine the Tur´an number of the family consisting of a blow-up of a cycle and a blow-up of a star in terms of the Tur´an number of the family consisting of a cycle,a star and linear forests with k edges.展开更多
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} .
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In this paper, we will explain the relevance of the starant graphs, graphs created by us in the year of 2002. They were basically circulant graphs with a star graph that connects to all the vertices of the circulant graphs from inside of them, but they did not exist as a separate object of study in the year of 2002, as for all we knew. We now know that they can be used to model even social networking interactions, and they do that job better than any other graph we could be trying to use there. With the development of our mathematical tools, lots of conclusions will be made much more believable and therefore will become much more likely to get support from the relevant industries when attached to new queries.
基金Supported by the National Nature Science Foundation of China(Grant Nos.11871329,11971298)。
文摘Let F={H_(1),...,H_(k)}(k≥1)be a family of graphs.The Tur´an number of the family F is the maximum number of edges in an n-vertex{H_(1),...,H_(k)}-free graph,denoted by ex(n,F)or ex(n,{H_(1),H_(2),...,H_(k)}).The blow-up of a graph H is the graph obtained from H by replacing each edge in H by a clique of the same size where the new vertices of the cliques are all different.In this paper we determine the Tur´an number of the family consisting of a blow-up of a cycle and a blow-up of a star in terms of the Tur´an number of the family consisting of a cycle,a star and linear forests with k edges.
