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Cycles and sorting index for matchings and restricted permutations
Cycles and sorting index matchings and restricted permutations Combinatorics
2012/6/25
We prove that the Mahonian-Stirling pairs of permutation statistics $(\sor, \cyc)$ and $(\inv, \mathrm{rlmin})$ are equidistributed on the set of permutations that correspond to arrangements of $n$ no...
Monochromatic cycles and the monochromatic circumference in 2-coloured graphs
Monochromatic cycles monochromatic circumference 2-coloured graphs
2011/9/21
Abstract: Li, Nikiforov and Schelp conjectured that a 2-edge coloured graph G with order n and minimal degree strictly greater than 3n/4 contains a monochromatic cycle of length l, for all l at least ...
On a Greedy 2-Matching Algorithm and Hamilton Cycles in Random Graphs with Minimum Degree at Least Three
Greedy 2-Matching Algorithm Hamilton Cycles Random Graphs Minimum Degree
2011/9/20
Abstract: We describe and analyse a simple greedy algorithm \2G\ that finds a good 2-matching $M$ in the random graph $G=G_{n,cn}^{\d\geq 3}$ when $c\geq 15$. A 2-matching is a spanning subgraph of ma...
On a conjecture of Erdos and Simonovits: Even Cycles
conjecture of Erdos and Simonovits Even Cycles Combinatorics
2011/9/19
Abstract: Let $\mc{F}$ be a family of graphs. A graph is {\em $\mc{F}$-free} if it contains no copy of a graph in $\mc{F}$ as a subgraph. A cornerstone of extremal graph theory is the study of the {\e...
Abstract: Every graph of size $q$ (the number of edges) and minimum degree $\delta$ is hamiltonian if $q\le\delta^2+\delta-1$. The result is sharp.