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108
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COMBINATORICS
2007
15 years 3 months ago
2007
In this paper, we prove that in a multigraph whose density Γ exceeds the maximum vertex degree ∆, the collection of minimal clusters (maximally dense sets of vertices) is cycle...
105
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COMBINATORICS
2007
15 years 3 months ago
2007
Suppose xm + axn is a permutation polynomial over Fp, where p > 5 is prime and m > n > 0 and a ∈ F∗ p. We prove that gcd(m−n, p−1) /∈ {2, 4}. In the special cas...
84
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COMBINATORICS
2007
15 years 3 months ago
2007
We present an infinite family of 3-connected non-bipartite graphs with chromatic roots in the interval (1, 2) thus resolving a conjecture of Jackson’s in the negative. In addit...
COMBINATORICS
2007
15 years 3 months ago
2007
In 1995, Hochberg, McDiarmid, and Saks proved that the vertex-bandwidth of the triangular grid Tn is precisely n + 1; more recently Balogh, Mubayi, and Pluh´ar posed the problem ...
114
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COMBINATORICS
2007
15 years 3 months ago
2007
In this note we present a short proof of the following result, which is a slight extension of a nice 2005 theorem by Kano and Yu. Let e be an edge of an rregular graph G. If G has...