Beata Orchel BIPARTITE EMBEDDING OF ( p , q ) - TREES

2-placement of (p, Q)-trees

Let G = (L,R; E) be a bipartite graph such that V (G) = L ∪ R, |L| = p and |R| = q. G is called (p, q)-tree if G is connected and |E(G)| = p + q − 1. Let G = (L, R;E) and H = (L′, R′;E′) be two (p, q)-tree. A bijection f : L ∪ R → L′ ∪ R′ is said to be a biplacement of G and H if f(L) = L′ and f(x)f(y) / ∈ E′ for every edge xy of G. A biplacement of G and its copy is called 2-placement of G. A ...

Placing bipartite graphs of small size II

In this paper we give all pairs of non mutually placeable (p, q)bipartite graphs G and H such that 2 ≤ p ≤ q, e(H) ≤ p and e(G) + e(H) ≤ 2p+ q − 1.

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...

Anti-proliferative effects of inositol hexaphosphate and verapamil on human colon cancer Caco-2 and HT-29 cells.

Mixed cycle-E-super magic decomposition of complete bipartite graphs

An H-magic labeling in a H-decomposable graph G is a bijection f : V (G) ∪ E(G) → {1, 2, ..., p + q} such that for every copy H in the decomposition, ΣνεV(H) f(v) +  ΣeεE(H) f(e) is constant. f is said to be H-E-super magic if f(E(G)) = {1, 2, · · · , q}. A family of subgraphs H1,H2, · · · ,Hh of G is a mixed cycle-decomposition of G if every subgraph Hi is isomorphic to some cycle Ck, for k ≥ ...