MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY 156(3) 521-544 2014年5月 [査読有り]
We introduce invariants of graphs embedded in S-3 which are related to the Wu invariant and the Simon invariant. Then we use our invariants to prove that certain graphs are intrinsically chiral, and to obtain lower bounds for the minimal crossing ...
NEW YORK JOURNAL OF MATHEMATICS 20 471-495 2014年 [査読有り]
We give a Conway-Gordon type formula for invariants of knots and links in a spatial complete four-partite graph K-3,K-3,K-1,K-1 in terms of the square of the linking number and the second coefficient of the Conway polynomial. As an application, we...
JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS 22(9) 1350048 2013年8月 [査読有り]
For every spatial embedding of each graph in the Petersen family, it is known that the sum of the linking numbers over all of the constituent 2-component links is congruent to 1 modulo 2. In this paper, we give an integral lift of this formula in ...
JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS 21(7) 1250067 2012年6月 [査読有り]
Conway-Gordon proved that for every spatial complete graph on six vertices, the sum of the linking numbers over all of the constituent 2-component links is congruent to 1 modulo 2, and for every spatial complete graph on seven vertices, the sum of...
Pacific Journal of Mathematics 252(2) 407-425 2011年 [査読有り]
We say that a graph is intrinsically knotted or completely 3-linked if every embedding of the graph into the 3-sphere contains a nontrivial knot or a 3-component link each of whose 2-component sublinks is nonsplittable. We show that a graph obtain...
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