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JCT
2008
84views more  JCT 2008»
13 years 10 months ago
Minimally non-Pfaffian graphs
We consider the question of characterizing Pfaffian graphs. We exhibit an infinite family of non-Pfaffian graphs minimal with respect to the matching minor relation. This is in sha...
Serguei Norine, Robin Thomas
CORR
2008
Springer
77views Education» more  CORR 2008»
13 years 10 months ago
Principal Graphs and Manifolds
In many physical statistical, biological and other investigations it is desirable to approximate a system of points by objects of lower dimension and/or complexity. For this purpo...
Alexander N. Gorban, Andrei Yu. Zinovyev
DM
2006
83views more  DM 2006»
13 years 10 months ago
A note on k-cop, l-robber games on graphs
We give an algorithmic characterisation of finite cop-win digraphs. The case of k > 1 cops and k l 1 robbers is then reduced to the one cop case. Similar characterisations are ...
Gena Hahn, Gary MacGillivray
COMBINATORICS
2006
98views more  COMBINATORICS 2006»
13 years 10 months ago
Restricted Walks in Regular Trees
Let T be the Cayley graph of a finitely generated free group F. Given two vertices in T consider all the walks of a given length between these vertices that at a certain time must...
Laura Ciobanu, Sasa Radomirovic
JCT
2008
85views more  JCT 2008»
13 years 10 months ago
Smith normal form and Laplacians
Let M denote the Laplacian matrix of a graph G. Associated with G is a finite group (G), obtained from the Smith normal form of M, and whose order is the number of spanning trees o...
Dino J. Lorenzini