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COMBINATORICS
1999
95views more  COMBINATORICS 1999»
14 years 9 months ago
Maximum Degree Growth of the Iterated Line Graph
Let k denote the maximum degree of the kth iterated line graph Lk(G). For any connected graph G that is not a path, the inequality k+1 2k - 2 holds. Niepel, Knor, and Solt
Stephen G. Hartke, Aparna W. Higgins
COMBINATORICS
1999
102views more  COMBINATORICS 1999»
14 years 9 months ago
Critical Subgraphs of a Random Graph
We prove that the threshold for a random graph to have a k-core is equal to the threshold for having a subgraph which meets a necessary condition of Gallai for being k-critical. 1...
Michael Molloy, Bruce A. Reed
COMBINATORICS
1999
77views more  COMBINATORICS 1999»
14 years 9 months ago
A Multiple Integral Evaluation Inspired by the Multi-WZ Method
We give an integral identity which was conjectured and proved by using the continuous version of the multi-WZ method. Submitted: May 25, 1999; Accepted: October 20, 1999. Mathemat...
Akalu Tefera
COMBINATORICS
2000
97views more  COMBINATORICS 2000»
14 years 9 months ago
Counting Lattice Paths by Narayana Polynomials
Let d(n) count the lattice paths from (0, 0) to (n, n) using the steps (0,1), (1,0), and (1,1). Let e(n) count the lattice paths from (0, 0) to (n, n) with permitted steps from th...
Robert A. Sulanke
COMBINATORICS
2004
94views more  COMBINATORICS 2004»
14 years 9 months ago
A Bijection Between Classes of Fully Packed Loops and Plane Partitions
It has recently been observed empirically that the number of FPL configurations with 3 sets of a, b and c nested arches equals the number of plane partitions in a box of size a
P. Di Francesco, Paul Zinn-Justin, Jean-Bernard Zu...