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We consider the Erd{H{o}}s - Faber - Lov{a}sz (EFL) conjecture for hypergraphs. This paper gives an upper bound for the chromatic number of $r$ regular linear hypergraphs $textbf{H}$ of size $n$. If $r ge 4$, $chi (textbf{H}) le 1.181n$ and if $r=3$, $chi(textbf{H}) le 1.281n$
The ErdH{o}s-Faber-Lov{a}sz conjecture (posed in 1972) states that the chromatic index of any linear hypergraph on $n$ vertices is at most $n$. In this paper, we prove this conjecture for every large $n$. We also provide stabili
In 1972, Erd{o}s - Faber - Lov{a}sz (EFL) conjectured that, if $textbf{H}$ is a linear hypergraph consisting of $n$ edges of cardinality $n$, then it is possible to color the vertices with $n$ colors so that no two vertices with the same color are in
We study the homological algebra of edge ideals of Erd{o}s-Renyi random graphs. These random graphs are generated by deleting edges of a complete graph on $n$ vertices independently of each other with probability $1-p$. We focus on some aspects of th
A graph is $P_8$-free if it contains no induced subgraph isomorphic to the path $P_8$ on eight vertices. In 1995, ErdH{o}s and Gy{a}rf{a}s conjectured that every graph of minimum degree at least three contains a cycle whose length is a power of two.
An $r$-uniform hypergraph ($r$-graph for short) is called linear if every pair of vertices belong to at most one edge. A linear $r$-graph is complete if every pair of vertices are in exactly one edge. The famous Brown-ErdH{o}s-Sos conjecture states t