The choice number of a graph G,denoted byχl(G) ,is the minimum number k such that if a list of k colors is given to each vertex of G,there is a vertex coloring of G where each vertex receives a color from its own l...The choice number of a graph G,denoted byχl(G) ,is the minimum number k such that if a list of k colors is given to each vertex of G,there is a vertex coloring of G where each vertex receives a color from its own listno matter whatthe lists are.In this paper,itis showed thatχl(G)≤ 3 for each plane graph of girth not less than 4 which contains no 6- ,7- and 9- cycles展开更多
A proper vertex coloring of a graph G is linear if the graph induced by the vertices of any two color classes is the union of vertex-disjoint paths. The linear chromatic number lc(G) of the graph G is the smallest num...A proper vertex coloring of a graph G is linear if the graph induced by the vertices of any two color classes is the union of vertex-disjoint paths. The linear chromatic number lc(G) of the graph G is the smallest number of colors in a linear coloring of G. In this paper, we give some upper bounds on linear chromatic number for plane graphs with respect to their girth, that improve some results of Raspaud and Wang (2009).展开更多
It is known that every triangle-free plane graph is 3-colorable.However,such a triangle-free plane graph may not be 3-choosable.In this paper,we prove that a triangle-free plane graph is 3-choosable if no 4-cycle in i...It is known that every triangle-free plane graph is 3-colorable.However,such a triangle-free plane graph may not be 3-choosable.In this paper,we prove that a triangle-free plane graph is 3-choosable if no 4-cycle in it is adjacent to a 4-or a 5-cycle.This improves some known results in this direction.展开更多
This paper considers an SIRS epidemic model that incorporates constant immigrati on rate, a general population size dependent contact rate and proportional tran sfer rate from the infective class to susceptible class...This paper considers an SIRS epidemic model that incorporates constant immigrati on rate, a general population size dependent contact rate and proportional tran sfer rate from the infective class to susceptible class.A threshold parameter σ is identified. If σ≤1, the disease free equilibrium is globally stab le. If σ>1, a unique endemic equilibrium is locally asymptotically stable. For two important special cases of mass action incidence and standard incidence, global stability of the endemic equilibrium is proved provided the threshold is larger than unity. Some previous results are extended and improved.展开更多
基金supported by the National Natural Science Foundation of China(1 0 0 0 1 0 35)
文摘The choice number of a graph G,denoted byχl(G) ,is the minimum number k such that if a list of k colors is given to each vertex of G,there is a vertex coloring of G where each vertex receives a color from its own listno matter whatthe lists are.In this paper,itis showed thatχl(G)≤ 3 for each plane graph of girth not less than 4 which contains no 6- ,7- and 9- cycles
基金supported by National Natural Science Foundation of China (Grant Nos. 10931003, 10801077)the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (Grant No. 08KJB110008).
文摘A proper vertex coloring of a graph G is linear if the graph induced by the vertices of any two color classes is the union of vertex-disjoint paths. The linear chromatic number lc(G) of the graph G is the smallest number of colors in a linear coloring of G. In this paper, we give some upper bounds on linear chromatic number for plane graphs with respect to their girth, that improve some results of Raspaud and Wang (2009).
基金supported by the Zhejiang Provincial Natural Science Foundation ofChina (Grant No. Y6090699)National Natural Science Foundation of China (Grant No. 10971198)ZhejiangInnovation Project (Grant No. T200905)
文摘It is known that every triangle-free plane graph is 3-colorable.However,such a triangle-free plane graph may not be 3-choosable.In this paper,we prove that a triangle-free plane graph is 3-choosable if no 4-cycle in it is adjacent to a 4-or a 5-cycle.This improves some known results in this direction.
基金Supported by the Science and Technology Foundation of Zhejiang University(1 0 70 0 0 - 54430 1 )
文摘This paper considers an SIRS epidemic model that incorporates constant immigrati on rate, a general population size dependent contact rate and proportional tran sfer rate from the infective class to susceptible class.A threshold parameter σ is identified. If σ≤1, the disease free equilibrium is globally stab le. If σ>1, a unique endemic equilibrium is locally asymptotically stable. For two important special cases of mass action incidence and standard incidence, global stability of the endemic equilibrium is proved provided the threshold is larger than unity. Some previous results are extended and improved.
