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Fractional Graph Theory: A Rational Approach to the Theory of Graphs
General Theory: Hypergraphs. Fractional Matching. Fractional Coloring. Fractional Edge Coloring. Fractional Arboricity and Matroid Methods. Fractional Isomorphism. Fractional Odds and Ends. Appendix.Expand
On the structure of the lattice of noncrossing partitions
TLDR
It is shown that the lattice of noncrossing (set) partitions is self-dual and that it admits a symmetric chain decomposition and several identities involving Catalan numbers emerge from the construction of the symmetricChain decomposition. Expand
Problems and Solutions
TLDR
This dissertation aims to provide a history of Hungarian literature and its critics from 1989 to 2002, a period chosen in order to explore its roots as well as specific cases up to and including the year in which its author, Tamás Erdélyi, died. Expand
Combinatorial Games under Auction Play
Abstract A Richman game is a combinatorial game in which, rather than alternating moves, the two players bid for the privilege of making the next move. The theory of such games is a hybrid betweenExpand
Undirected Edge Geography
TLDR
This work shows that the decision problem of determining whether a position in this game of edge geography is a win for the first player is PSPACE-complete, and provides a linear algebraic characterization of the P- and N-positions. Expand
Fractional isomorphism of graphs
TLDR
It is proved that quadratic fractional isomorphicism is the same as isomorphism and semi-isomorphism is related to is morphism of bipartite graphs. Expand
The fractional chromatic number of mycielski's graphs
TLDR
This article calculates the fractional chromatic number of Gn and shows that this sequence of numbers satisfies the unexpected recurrence an+1 = an + (1/an). Expand
Richman games
A Richman game is a combinatorial game in which, rather than alternating moves, the two players bid for the privilege of making the next move. We find optimal strategies for both the case where aExpand
Sequential Compounds of Combinatorial Games
TLDR
The theory of these sequential compounds is explored and the outcomes and Grundy values of certain games of this form of combinatorial games are determined. Expand
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