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2010
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15 years 20 days ago
Unavoidable topological minors of infinite graphs
A graph G is loosely-c-connected, or -c-connected, if there exists a number d depending on G such that the deletion of fewer than c vertices from G leaves precisely one infinite co...
Carolyn Chun, Guoli Ding
93
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DM
2010
134views more  DM 2010»
15 years 20 days ago
The discrepancy of the lex-least de Bruijn sequence
We answer the following question of R. L. Graham: What is the discrepancy of the lexicographically-least binary de Bruijn sequence? Here, "discrepancy" refers to the max...
Joshua Cooper, Christine E. Heitsch
99
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DM
2010
90views more  DM 2010»
15 years 20 days ago
The firefighter problem for cubic graphs
We show that the firefighter problem is NP-complete for cubic graphs. We also show that given a rooted tree of maximum degree three in which every leaf is the same distance from t...
Andrew King, Gary MacGillivray
101
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DM
2010
86views more  DM 2010»
14 years 10 months ago
On the simple connectedness of hyperplane complements in dual polar spaces, II
Suppose is a dual polar space of rank n and H is a hyperplane of . Cardinali, De Bruyn and Pasini have already shown that if n 4 and the line size is greater than or equal to fo...
Justin McInroy, Sergey Shpectorov
85
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DM
2010
107views more  DM 2010»
15 years 20 days ago
An analytic approach to stability
The stability method is very useful for obtaining exact solutions of many extremal graph problems. Its key step is to establish the stability property which, roughly speaking, sta...
Oleg Pikhurko