36 research outputs found
Tur\`an numbers of Multiple Paths and Equibipartite Trees
The Tur\'an number of a graph H, ex(n;H), is the maximum number of edges in
any graph on n vertices which does not contain H as a subgraph. Let P_l denote
a path on l vertices, and kP_l denote k vertex-disjoint copies of P_l. We
determine ex(n, kP_3) for n appropriately large, answering in the positive a
conjecture of Gorgol. Further, we determine ex (n, kP_l) for arbitrary l, and n
appropriately large relative to k and l. We provide some background on the
famous Erd\H{o}s-S\'os conjecture, and conditional on its truth we determine
ex(n;H) when H is an equibipartite forest, for appropriately large n.Comment: 17 pages, 13 figures; Updated to incorporate referee's suggestions;
minor structural change
Generalized Tur\'an problems for disjoint copies of graphs
Given two graphs and , the maximum possible number of copies of in
an -free graph on vertices is denoted by . We investigate the
function , where denotes vertex disjoint copies of a fixed
graph . Our results include cases when is a complete graph, cycle or a
complete bipartite graph.Comment: 18 pages. There was a wrong statement in the first version, it is
corrected no
On the Turan number of forests
The Turan number of a graph H, ex(n,H), is the maximum number of edges in a
graph on n vertices which does not have H as a subgraph. We determine the Turan
number and find the unique extremal graph for forests consisting of paths when
n is sufficiently large. This generalizes a result of Bushaw and Kettle [
Combinatorics, Probability and Computing 20:837--853, 2011]. We also determine
the Turan number and extremal graphs for forests consisting of stars of
arbitrary order
Rainbow Generalizations of Ramsey Theory - A Dynamic Survey
In this work, we collect Ramsey-type results concerning rainbow edge colorings of graphs
Rainbow Generalizations of Ramsey Theory - A Dynamic Survey
In this work, we collect Ramsey-type results concerning rainbow edge colorings of graphs
Rainbow Generalizations of Ramsey Theory - A Dynamic Survey
In this work, we collect Ramsey-type results concerning rainbow edge colorings of graphs