A new bound on maximum genus of simple graphs

作者：Lv, Shengxiang^*; Liu, Yanpei

来源：Ars Combinatoria, 2011, 98: 7-14.

• Up-embeddability
• Maximum genus
• Betti deficiency number
• Moore bound

Let G be a connected simple graph with girth g and minimal degree delta >= 3. If G is not up-embeddable, then, when G is 1-edge connected,
gamma(M) (G) >= D(1)(delta, g) - 2/2D(1)(delta, g) - 1 beta(G) + D(1)(delta, g) + 1/2D(1)(delta, g) - 1;
when G is k(k = 2, 3)-edge connected,
gamma(M) (G) >= D(k)(delta, g) - 1/2D(k)(delta, g)beta(G) + D(k)(delta, g) + 1/2D(k)(delta, g).
D(k)(delta, g)(k = 1,2,3) are increasing functions on delta and g.

• 出版日期2011-1
• 单位北京交通大学; 湖南科技大学