Results 41 to 50 of about 92,446 (202)
Cohen-macaulay bipartite graphs [PDF]
Archiv der Mathematik, 1997 Let \(G\) be a graph on the vertex set \(V=\{x_1, \dots, x_n\}\). Let \(k\) be a field and let \(R\) be the polynomial ring \(k[x_1, \dots, x_n]\). The graph ideal \(I(G)\), associated to \(G\), is the ideal of \(R\) generated by the set of square-free monomials \(x_ix_j\) so that \(x_i\) is adjacent to \(x_j\). The graph \(G\) is Cohen-Macaulay over \(
Estrada, Mario, Villarreal, Rafael H.
openaire +2 more sources
Bipartite embedding of (p,q)-trees [PDF]
Opuscula Mathematica, 2006 A bipartite graph \(G=(L,R;E)\) where \(V(G)=L\cup R\), \(|L|=p\), \(|R| =q\) is called a \((p,q)\)-tree if \(|E(G)|=p+q-1\) and \(G\) has no cycles. A bipartite graph \(G=(L,R;E)\) is a subgraph of a bipartite graph \(H=(L',R';E')\) if \(L\subseteq L'\)
Beata Orchel
doaj
The Median Problem on k-Partite Graphs
Discussiones Mathematicae Graph Theory, 2015 In a connected graph G, the status of a vertex is the sum of the distances of that vertex to each of the other vertices in G. The subgraph induced by the vertices of minimum (maximum) status in G is called the median (anti-median) of G.
Pravas Karuvachery, Vijayakumar Ambat
doaj +1 more source
Homomorphisms of binary Cayley graphs
, 2015 A binary Cayley graph is a Cayley graph based on a binary group. In 1982, Payan proved that any non-bipartite binary Cayley graph must contain a generalized Mycielski graph of an odd-cycle, implying that such a graph cannot have chromatic number 3.
Beaudou, Laurent +2 more
core +3 more sources
Enumeration of Bipartite Graphs and Bipartite Blocks [PDF]
The Electronic Journal of Combinatorics, 2014 We use the theory of combinatorial species to count unlabelled bipartite graphs and bipartite blocks (nonseparable or 2-connected graphs). We start with bicolored graphs, which are bipartite graphs that are properly colored in two colors. The two-element group $\mathfrak{S}_2$ acts on these graphs by switching the colors, and connected bipartite graphs
Gainer-Dewar, Andrew, Gessel, Ira M.
openaire +3 more sources
A Note on the Permanental Roots of Bipartite Graphs
Discussiones Mathematicae Graph Theory, 2014 It is well-known that any graph has all real eigenvalues and a graph is bipartite if and only if its spectrum is symmetric with respect to the origin.
Zhang Heping, Liu Shunyi, Li Wei
doaj +1 more source
Antifactors of regular bipartite graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 Let $G=(X,Y;E)$ be a bipartite graph, where $X$ and $Y$ are color classes and $E$ is the set of edges of $G$. Lov\'asz and Plummer \cite{LoPl86} asked whether one can decide in polynomial time that a given bipartite graph $G=(X,Y; E)$ admits a 1-anti ...
Hongliang Lu, Wei Wang, Juan Yan
doaj +1 more source
Journal of Combinatorial Theory, Series B, 2012 27 pages, small revisions from previous version, this version appears in Journal of Combinatorial Theory Series ...
Engbers, John, Galvin, David
openaire +3 more sources
The Connectivity of a Bipartite Graph and Its Bipartite Complementary Graph [PDF]
Parallel Processing Letters, 2020 In 1956, Nordhaus and Gaddum gave lower and upper bounds on the sum and the product of the chromatic number of a graph and its complement, in terms of the order of the graph. Since then, any bound on the sum and/or the product of an invariant in a graph [Formula: see text] and the same invariant in the complement [Formula: see text] of [Formula: see ...
Yingzhi Tian, Huaping Ma, Liyun Wu
openaire +3 more sources
Bipartite Diametrical Graphs of Diameter 4 and Extreme Orders
International Journal of Mathematics and Mathematical Sciences, 2008 We provide a process to extend any bipartite diametrical graph of diameter 4 to an 𝑆-graph of the same diameter and partite sets. For a bipartite diametrical graph of diameter 4 and partite sets 𝑈 and 𝑊, where 2𝑚=|𝑈|≤|𝑊|, we prove that 2𝑚 is a sharp ...
Salah Al-Addasi, Hasan Al-Ezeh
doaj +1 more source