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Prime component-preservingly amphicheiral link with odd minimal crossing number
component-preservingly amphicheiral link minimal crossing number Tait's conjecture
2012/3/1
For every odd integer $c\ge 21$, we raise an example of a prime component-preservingly amphicheiral link with minimal crossing number $c$.
Twisted Lefschetz number and Nielsen number
Lefschetz number Nielsen number Algebraic Topology
2011/9/21
Abstract: We study the twisted Lefschetz number, which is a generalization of classical Lefschetz number. A formula in terms of homology with local coefficients is given. We then propose a method to e...
Computing the crosscap number of a knot using integer programming and normal surfaces
integer programming normal surfaces crosscap number of a knot Geometric Topology
2011/9/5
Abstract: The crosscap number of a knot is an invariant describing the non-orientable surface of smallest genus that the knot bounds. Unlike knot genus (its orientable counterpart), crosscap numbers a...
Upper bounds for the bondage number of graphs on topological surfaces
Bondage number Domination number Topological surface
2011/2/22
The bondage number b(G) of a graph G is the smallest number of edges of G whose removal from G results in a graph having the domination number larger than that of G. We show that, for a graph G having...
The adjacent vertex distinguishing total chromatic number
The adjacent vertex distinguishing total chromatic number
2010/12/2
A well-studied concept is that of the total chromatic number. A proper total colouring of a graph is a colouring of both vertices and edges so that every pair of adjacent vertices receive di erent col...
Point sets that minimize $(\le k)$-edges, $3$-decomposable drawings, and the rectilinear crossing number of $K_{30}$
k–edges 3-decomposability rectilinear crossing number
2010/12/10
There are two properties shared by all known crossing-minimizing geometric drawings of Kn, for n a multiple of 3.First, the underlying n-point set of these drawings has exactly 3k+2
2(≤ k)...