Improved bounds for the number of forests and acyclic orientations in the square lattice.
In the Square of Graphs, Hamiltonicity and Pancyclicity, Hamiltonian Connectedness and Panconnectedness Are Equivalent Concepts.
Independence number and disjoint theta graphs.
Independent cycles and paths in bipartite balanced graphs
Bipartite graphs G = (L,R;E) and H = (L’,R’;E’) are bi-placeabe if there is a bijection f:L∪R→ L’∪R’ such that f(L) = L’ and f(u)f(v) ∉ E’ for every edge uv ∈ E. We prove that if G and H are two bipartite balanced graphs of order |G| = |H| = 2p ≥ 4 such that the sizes of G and H satisfy ||G|| ≤ 2p-3 and ||H|| ≤ 2p-2, and the maximum degree of H is at most 2, then G and H are bi-placeable, unless G and H is one of easily recognizable couples of graphs. This result implies easily that for integers...
Induced paths in twin-free graphs.
Induced subgraphs with the same order and size
Induced-paired domatic numbers of graphs
A subset of the vertex set of a graph is called dominating in , if each vertex of either is in , or is adjacent to a vertex of . If moreover the subgraph of induced by is regular of degree 1, then is called an induced-paired dominating set in . A partition of , each of whose classes is an induced-paired dominating set in , is called an induced-paired domatic partition of . The maximum number of classes of an induced-paired domatic partition of is the induced-paired domatic...
Intersection number of a graph
Interval edge-coloring of caterpillars with hairs of arbitrary length
Irreducible coverings by cliques and Sperner's theorem.