A bracket polynomial for graphs, IV. Undirected Euler circuits, graph-links and multiply marked graphs

In earlier work we introduced the graph bracket polynomial of graphs with marked vertices, motivated by the fact that the Kauffman bracket of a link diagram D is determined by a looped, marked version of the interlacement graph associated to a directed Euler system of the universe graph of D. Here we extend the graph bracket to graphs whose vertices may carry different kinds of marks, and we show how multiply marked graphs encode interlacement with respect to arbitrary (undirected) Euler systems. The extended machinery brings together the earlier version and the graph-links of Ilyutko and Manturov [J. Knot Theory Ramifications 18 (2009) 791-823]. The greater flexibility of the extended bracket also allows for a recursive description much simpler than that of the earlier version.

Title	A bracket polynomial for graphs, IV. Undirected Euler circuits, graph-links and multiply marked graphs
Creator	Traldi, Lorenzo
Publisher	Journal of Knot Theory and Its Ramifications
Academic Department	Mathematics
Division	Natural Sciences
Organization	Lafayette College
Date Issued	August 2011
Date Available	2015-05-06T17:35:58Z
Type	Article
Language	English
Keyword	interlacement
	graph
	circuit partition
	Jones polynomial
	Reidemeister move
	graph-link
	virtual link
	Kauffman bracket
	local complement
Bibliographic Citation	Traldi, L. (2011 Aug.) "A bracket polynomial for graphs, IV. Undirected Euler circuits, graph-links and multiply marked graphs." Journal of Knot Theory and Its Ramifications 20 (8): 1093-1128.
Standard Identifier	Handle 10385/1873
Standard Identifier	DOI 10.1142/S0218216511009157
Permalink	http://hdl.handle.net/10385/1873
Rights Statement	In Copyright
Rights Holders	World Scientific Publishing Company