Add to ORKGIn the 1960s, Erdős and Gallai conjectured that the edge set of every graph on n vertices can be partitioned into O(n) cycles and edges. They observed that one can easily get an O(nlogn) upper bound by repeatedly removing the edges of the longest cycle. We make the first progress on this problem, showing that O(nloglogn) cycles and edges suffice. We also prove the Erdős‐Gallai conjecture for random graphs and for graphs with linear minimum degree
We prove that there is $c>0$ such that for all sufficiently large $n$, if $T_1,\dots,T_n$ are any tr...
AbstractThe path number p(G) of a graph G is the minimum number of paths needed to partition the edg...
AbstractLet G be a connected simple graph on n vertices. Gallai's conjecture asserts that the edges ...
In the 1960s, Erdős and Gallai conjectured that the edge set of every graph on n vertices can be par...
In the 1960s, Erdős and Gallai conjectured that the edge set of every graph on n vertices can be par...
In the 1960s, Erdős and Gallai conjectured that the edge set of every graph on n vertices can be par...
In the 1960s, Erdős and Gallai conjectured that the edge set of every graph on n vertices can be par...
In the 1960s, Erdős and Gallai conjectured that the edge set of every graph on n vertices can be par...
In the 1960's, Erd\H{o}s and Gallai conjectured that the edges of any $n$-vertex graph can be decomp...
In the 1960's, Erdős and Gallai conjectured that the edges of any n-vertex graph can be decomposed i...
Over 50 years ago, Erdős and Gallai conjectured that the edges of every graph on n vertices can be d...
Given an undirected graph G with n nodes and m edges, we address the problem of finding a largest co...
AbstractWe prove that every connected graph onnvertices can be covered by at mostn/2+O(n3/4) paths. ...
In his seminal 1976 paper, P\'osa showed that for all $p\geq C\log n/n$, the binomial random graph $...
AbstractLet G be a connected simple graph on n vertices. Gallai's conjecture asserts that the edges ...
We prove that there is $c>0$ such that for all sufficiently large $n$, if $T_1,\dots,T_n$ are any tr...
AbstractThe path number p(G) of a graph G is the minimum number of paths needed to partition the edg...
AbstractLet G be a connected simple graph on n vertices. Gallai's conjecture asserts that the edges ...
In the 1960s, Erdős and Gallai conjectured that the edge set of every graph on n vertices can be par...
In the 1960s, Erdős and Gallai conjectured that the edge set of every graph on n vertices can be par...
In the 1960s, Erdős and Gallai conjectured that the edge set of every graph on n vertices can be par...
In the 1960s, Erdős and Gallai conjectured that the edge set of every graph on n vertices can be par...
In the 1960s, Erdős and Gallai conjectured that the edge set of every graph on n vertices can be par...
In the 1960's, Erd\H{o}s and Gallai conjectured that the edges of any $n$-vertex graph can be decomp...
In the 1960's, Erdős and Gallai conjectured that the edges of any n-vertex graph can be decomposed i...
Over 50 years ago, Erdős and Gallai conjectured that the edges of every graph on n vertices can be d...
Given an undirected graph G with n nodes and m edges, we address the problem of finding a largest co...
AbstractWe prove that every connected graph onnvertices can be covered by at mostn/2+O(n3/4) paths. ...
In his seminal 1976 paper, P\'osa showed that for all $p\geq C\log n/n$, the binomial random graph $...
AbstractLet G be a connected simple graph on n vertices. Gallai's conjecture asserts that the edges ...
We prove that there is $c>0$ such that for all sufficiently large $n$, if $T_1,\dots,T_n$ are any tr...
AbstractThe path number p(G) of a graph G is the minimum number of paths needed to partition the edg...
AbstractLet G be a connected simple graph on n vertices. Gallai's conjecture asserts that the edges ...