Add to ORKGWe define a new class of graphs called fair sharing graphs and prove that every three longest paths in a fair sharing graph share a common vertex. This verifies that the well-known conjecture that every three longest paths in a connected graph share a common vertex is true in this class of graphs. Mathematics Subject Classification: 05C3
Erdős–Faber–Lovász conjecture states that if a graph G is a union of the n edge-disjoint copies of c...
For given integers k, l we ask whether every large graph with a sufficiently small number of k-cliqu...
In this note we present two graphs embeddable into the equilateral triangular lattice and satisfying...
Abstract. It is well known that any two longest paths in a connected graph share a vertex. It is als...
International audienceIn 1966, T. Gallai asked whether every connected graph has a ver-tex that appe...
It is easy to see that in a connected graph any 2 longest paths have a vertex in common. For k >= 7,...
In 1966 Gallai asked whether all longest paths in a connected graph have nonempty intersec-tion. Thi...
summary:A maximum matching of a graph $G$ is a matching of $G$ with the largest number of edges. The...
summary:In 1966, Gallai conjectured that all the longest paths of a connected graph have a common ve...
AbstractA graph is said to have property I if every independent set of its vertices has a common nei...
Let τ(G) denote the number of vertices in a longest path of the graph G and let k₁ and k₂ be positiv...
Given a non empty set S of vertices of a graph, the partiality of a vertex with respect to S is the ...
It is a well known fact in graph theory that in a connected graph any two longest paths must have a ...
AbstractThe detour order of a graph G, denoted by τ(G), is the order of a longest path in G. The Pat...
1 There is a unique friendship two-graph? Definition 1 A friendship graph is a graph in which every ...
Erdős–Faber–Lovász conjecture states that if a graph G is a union of the n edge-disjoint copies of c...
For given integers k, l we ask whether every large graph with a sufficiently small number of k-cliqu...
In this note we present two graphs embeddable into the equilateral triangular lattice and satisfying...
Abstract. It is well known that any two longest paths in a connected graph share a vertex. It is als...
International audienceIn 1966, T. Gallai asked whether every connected graph has a ver-tex that appe...
It is easy to see that in a connected graph any 2 longest paths have a vertex in common. For k >= 7,...
In 1966 Gallai asked whether all longest paths in a connected graph have nonempty intersec-tion. Thi...
summary:A maximum matching of a graph $G$ is a matching of $G$ with the largest number of edges. The...
summary:In 1966, Gallai conjectured that all the longest paths of a connected graph have a common ve...
AbstractA graph is said to have property I if every independent set of its vertices has a common nei...
Let τ(G) denote the number of vertices in a longest path of the graph G and let k₁ and k₂ be positiv...
Given a non empty set S of vertices of a graph, the partiality of a vertex with respect to S is the ...
It is a well known fact in graph theory that in a connected graph any two longest paths must have a ...
AbstractThe detour order of a graph G, denoted by τ(G), is the order of a longest path in G. The Pat...
1 There is a unique friendship two-graph? Definition 1 A friendship graph is a graph in which every ...
Erdős–Faber–Lovász conjecture states that if a graph G is a union of the n edge-disjoint copies of c...
For given integers k, l we ask whether every large graph with a sufficiently small number of k-cliqu...
In this note we present two graphs embeddable into the equilateral triangular lattice and satisfying...