Results 231 to 240 of about 96,628 (243)

Bipartite graphs as polynomials and polynomials as bipartite graphs

Journal of Algebra and Its Applications, 2020
The aim of this paper is to show that any finite undirected bipartite graph can be considered as a polynomial [Formula: see text], and any directed finite bipartite graph can be considered as a polynomial [Formula: see text], and vise verse. We also show that the multiplication in the semirings [Formula: see text], [Formula: see text] corresponds to an
Andrey Grinblat, Viktor Lopatkin
openaire   +2 more sources

On Hamiltonian bipartite graphs

Israel Journal of Mathematics, 1963
Various sufficient conditions for the existence of Hamiltonian circuits in ordinary graphs are known. In this paper the analogous results for bipartite graphs are obtained.
J. Moon, J. Moon, L. Moser, L. Moser
openaire   +3 more sources

Bichromaticity of bipartite graphs [PDF]

Journal of Graph Theory, 1985
AbstractLet B be a bipartite graph with edge set E and vertex bipartition M, N. The bichromaticity β(B) is defined as the maximum number β such that a complete bipartite graph on β vertices is obtainable from B by a sequence of identifications of vertices of M or vertices of N. Let μ = max{∣M∣, ∣N∣}. Harary, Hsu, and Miller proved that β(B) ≥ μ + 1 and
openaire   +1 more source

Bipartite Coverings of Graphs

Combinatorics, Probability and Computing, 1997
In this note we give a probabilistic proof of the existence of an n-vertex graph Gn, n=1, 2, [ctdot ], such that, for some constant c>0, the edges of Gn cannot be covered by n−c log n complete bipartite subgraphs of Gn. This result improves a previous bound due to F. R. K. Chung and is the best possible up to a constant.
Vojtech Rödl, Andrzej Ruciński
openaire   +2 more sources

Graphoidal bipartite graphs

Graphs and Combinatorics, 1994
For many years a characterization of those graphs \(G\) so that \(G\cong L(H)\), where \(L(H)\) is the line graph of the graph \(H\), has been known. The authors generalize this notion as follows. A graphoidal cover \(\psi_ G\) of \(G\) is a partition of \(E(G)\) into paths so that each vertex is the interior vertex of at most one path.
C. Pakkiam, Subramanian Arumugam
openaire   +2 more sources

Locally bipartite graphs [PDF]

Mathematical Notes of the Academy of Sciences of the USSR, 1988
The solution of the following problem is given: How many edges \(\mu(n; K_{p,p+q})\) can an \(n\)-vertex graph have if each of its \((2p+q)\)-vertex subgraphs is embeddable in the complete bipartite graph \(K_{p,p+q}\)?
B. S. Stechkin, B. S. Stechkin
openaire   +1 more source

Packing two bipartite graphs into a complete bipartite graph

Journal of Graph Theory, 1997
A bipartite graph \(G\) admits an \((a,b)\)-bipartition if \(G\) has a bipartition \((X,Y)\) such that \(|X|=a\) and \(|Y|=b\). Two bipartite graphs \(G\) and \(H\) are compatible if, for some integers \(a\) and \(b\), both \(G\) and \(H\) admit an \((a,b)\)-bipartition. In the paper it is proved that any two compatible \(C_4\)-free bipartite graphs of
openaire   +3 more sources

Embeddings of bipartite graphs

Journal of Graph Theory, 1983
AbstractIf G is a bipartite graph with bipartition A, B then let Gm,n(A, B) be obtained from G by replacing each vertex a of A by an independent set a1, …, am, each vertex b of B by an independent set b1,…, bn, and each edge ab of G by the complete bipartite graph with edges aibj (1 ≤ i ≤ m and 1 ≤ j ≤ n).
T. D. Parsons, Mohammed Abu-Sbeih
openaire   +2 more sources

On packing bipartite graphs

Combinatorica, 1992
Two simple graphs \(G\) and \(H\) can be packed if \(G\) is isomorphic to a subgraph of the complement \(\overline H\) of \(H\). A sufficient condition is known for the existence of packing in terms of the product of the maximal degrees of \(G\) and \(H\).
Mario Szegedy, Péter Hajnal
openaire   +3 more sources