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EJC
2006
13 years 11 months ago
A note on Ramsey numbers with two parameters
1 The Ramsey number R(G1, G2) is the smallest integer p such that for any graph G on p vertices2 either G contains G1 or G contains G2, where G denotes the complement of G. In this...
Yi Ru Huang, Jian Sheng Yang, Kemin Zhang
EJC
2006
13 years 11 months ago
Hamiltonicity of digraphs for universal cycles of permutations
The digraphs P(n, k) have vertices corresponding to length k permutations of an n set and arcs corresponding to (k + 1) permutations. Answering a question of Starling, Klerlein, K...
Garth Isaak
EJC
2006
13 years 11 months ago
Homogeneous factorisations of graphs and digraphs
Michael Giudici, Cai Heng Li, Primoz Potocnik, Che...
EJC
2006
13 years 11 months ago
Two oiseau decompositions of permutations and their application to Eulerian calculus
: Two transformations are constructed that map the permutation group onto a well-defined subset of a partially commutative monoid generated by the so-called oiseaux. Those transfor...
Dominique Foata, Arthur Randrianarivony
EJC
2006
13 years 11 months ago
The topology of the independence complex
We introduce a large self-dual class of simplicial complexes for which we show that each member complex is contractible or homotopy equivalent to a sphere. Examples of complexes i...
Richard Ehrenborg, Gábor Hetyei
EJC
2006
13 years 11 months ago
Parity reversing involutions on plane trees and 2-Motzkin paths
The problem of counting plane trees with n edges and an even or an odd number of leaves has been recently studied by Eu, Liu and Yeh, in connection with an identity on coloring ne...
William Y. C. Chen, Louis W. Shapiro, Laura L. M. ...
EJC
2006
13 years 11 months ago
An iterative-bijective approach to generalizations of Schur's theorem
Abstract. We start with a bijective proof of Schur's theorem due to Alladi and Gordon and describe how a particular iteration of it leads to some very general theorems on colo...
Sylvie Corteel, Jeremy Lovejoy
EJC
2006
13 years 11 months ago
Old and young leaves on plane trees
Abstract. A leaf of a plane tree is called an old leaf if it is the leftmost child of its parent, and it is called a young leaf otherwise. In this paper we enumerate plane trees wi...
William Y. C. Chen, Emeric Deutsch, Sergi Elizalde