Link prediction is a crucial problem in the analysis of graph-structured data, and graph neural networks (GNNs) have proven to be effective addressing this problem. However, computational temporal costs associated with large-scale graphs remain concern. This study introduces novel method for link called Sparse Subgraph Prediction Based on Adaptive Attention (SSP-AA). The generates sparse subgra...

For a class $$\mathcal {G}$$ of graphs, the problem Subgraph Complement to asks whether one can find subset S vertices input graph G such that complementing subgraph induced by in results . We investigate complexity when is H-free for H being complete graph, star, path, or cycle. obtain following results: Further, we prove these hard problems do not admit subexponential-time algorithms (algorit...

Given a graph G and k∈N, we introduce the following game played in G. Each round, Alice colours an uncoloured vertex of red, then Bob one blue (if any remain). Once every is coloured, wins if there connected red component order at least k, otherwise, wins. This Maker-Breaker version Largest Connected Subgraph introduced [Bensmail et al., The largest subgraph game, Algorithmica 84 (9) (2022) 253...

The k-fold clique transversal problem is to locate a minimum set of vertices of a graph such that every maximal clique has at least k elements of. The maximum h-colourable subgraph problem is to nd a maximum subgraph of a graph which is h-colourable. We show that the k-fold clique transversal problem and the maximum h-colourable subgraph problem are polynomially solvable on balanced graphs. We ...

Some versions of the maximum common subgraph problem are studied and approximation algorithms are given. The maximum bounded common induced subgraph problem is shown to be Max SNP-hard and the maximum unbounded common induced subgraph problem is shown to be as hard to approximate as the maximum independent set problem. The maximum common induced connected subgraph problem is still harder to app...

A graph g is called a maximum common subgraph of two graphs, g 1 and g 2 , if there exists no other common subgraph of g 1 and g2 that has more nodes than g. For the maximum common subgraph problem, exact and inexact algorithms are known from the literature. Nevertheless, until now no effort has been done for characterizing their performance, mainly for the lack of a large database of graphs. I...

Labeled graphs are widely used to model complex data in many domains, so subgraph querying has been attracting more and more attention from researchers around the world. Unfortunately, subgraph querying is very time consuming since it involves subgraph isomorphism testing that is known to be an NP-complete problem. In this paper, we propose a novel coding method for subgraph querying that is ba...

For every k ∈ N0, we consider graphs in which for any induced subgraph, ∆ ≤ χ − 1 + k holds, and call this family of graphs Υk, where ∆ is the maximum degree and χ is the chromatic number of the subgraph. We give a finite forbidden induced subgraph characterization for every k. The results are compared to those given in [6], where the graphs in which for any induced subgraph, ∆ ≤ ω − 1 + k hold...