Abstract The early concept of knowledge graph originates from the idea Semantic Web, which aims at using structured graphs to model world and record relationships that exist between things. Currently publishing bases as open data on Web has gained significant attention. In China, CIPS(Chinese Information Processing Society) launched OpenKG in 2015 foster development Chinese Open Knowledge Graph...

A co-bipartite chain graph is a co-bipartite graph in which the neighborhoods of the vertices in each clique can be linearly ordered with respect to inclusion. It is known that the maximum cut problem (MaxCut) is NP-hard in co-bipartite graphs [3]. We consider MaxCut in co-bipartite chain graphs. We first consider the twin-free case and present an explicit solution. We then show that MaxCut is ...

We examine the simultaneous embedding with fixed edges problem for two planar graphs G1 and G2 with the focus on their intersection S = G1∩G2. In particular, we will present the complete set of intersection graphs S that guarantee a simultaneous embedding with fixed edges for (G1, G2). More formally, we define the subset ISEFE of all planar graphs as follows: A graph S lies in ISEFE if every pa...

We prove that the unique decomposition of connected graphs defined by Tutte is definable by formulas of Monadic Second-Order Logic. This decomposition has two levels: every connected graph is a tree of "2-connected components" called blocks ; every 2-connected graph is a tree of so-called 3-blocks. Our proof uses 2dags which are certain acyclic orientations of the considered graphs. We obtain a...

The rank-width is a graph parameter related in terms of fixed functions to cliquewidth but more tractable. Clique-width has nice algorithmic properties, but no good “minor” relation is known analogous to graph minor embedding for tree-width. In this paper, we discuss the vertex-minor relation of graphs and its connection with rank-width. We prove a relationship between vertex-minors of bipartit...

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The switching model is a Markov chain approach to sample graphs with fixed degree sequence uniformly at random. The recently invented Curveball algorithm [35] for bipartite graphs applies several switches simultaneously (‘trades’). Here, we introduce Curveball algorithms for simple (un)directed graphs which use single or simultaneous trades. We show experimentally that these algorithms converge...

We provide polynomial-time algorithms for counting the number of perfect matchings and the number of matchings in chain graphs, cochain graphs, and threshold graphs. These algorithms are based on newly developed subdivision schemes that we call a recursive decomposition. On the other hand, we show the #P-completeness for counting the number of perfect matchings in chordal graphs, split graphs a...

The vertex Padmakar-Ivan (PIv) index of a graph G was introduced as the sum over all edges e = uv of G of the number of vertices which are not equidistant to the vertices u and v. In this paper we provide an analogue to the results of T. Mansour and M. Schork [The PI index of bridge and chain graphs, MATCH Commun. Math. Comput. Chem. 61 (2009) 723-734]. Two efficient formulas for calculating th...