Related papers: Fitch Graph Completion

Graph foundation models (GFMs) aim to reuse a single backbone across diverse graph domains, yet their transfer is often uneven and can exhibit negative transfer. While most prior work improves transfer through architectural or adaptation…

Social networks exhibit strikingly systematic patterns across a wide range of human contexts. While genetic variation accounts for a significant portion of the variation in many complex social behaviors, the heritability of egocentric…

Let $\{D_M\}_{M\geq 0}$ be the $n$-vertex random directed graph process, where $D_0$ is the empty directed graph on $n$ vertices, and subsequent directed graphs in the sequence are obtained by the addition of a new directed edge uniformly…

In graph realization problems one is given a degree sequence and the task is to decide whether there is a graph whose vertex degrees match to the given sequence. This realization problem is known to be polynomial-time solvable when the…

A 2-switch is an edge addition/deletion operation that changes adjacencies in the graph while preserving the degree of each vertex. A well known result states that graphs with the same degree sequence may be changed into each other via…

A graph is edge-transitive if the natural action of its automorphism group on its edge set is transitive. An automorphism of a graph is semiregular if all of the orbits of the subgroup generated by this automorphism have the same length.…

If P is a hereditary property then we show that, for the existence of a perfect f-factor, P is a sufficient condition for countable graphs and yields a sufficient condition for graphs of size aleph_1. Further we give two examples of a…

A longstanding open question of Archdeacon and Craft asks whether every complete graph has a minimum genus embedding with at most one nontriangular face. We exhibit such an embedding for each complete graph except $K_8$, the complete graph…

Motivation: Millions of genes in the modern species belong to only thousands of `gene families'. A gene family includes instances of the same gene in different species (orthologs) and duplicate genes in the same species (paralogs). Genes…

A graph is distance-hereditary if for any pair of vertices, their distance in every connected induced subgraph containing both vertices is the same as their distance in the original graph. The Distance-Hereditary Vertex Deletion problem…

In phylogenetics, tree-based networks are used to model and visualize the evolutionary history of species where reticulate events such as horizontal gene transfer have occurred. Formally, a tree-based network $N$ consists of a phylogenetic…

We study "positive" graphs that have a nonnegative homomorphism number into every edge-weighted graph (where the edgeweights may be negative). We conjecture that all positive graphs can be obtained by taking two copies of an arbitrary…

The association of a given human phenotype to a genetic variant remains a critical challenge for biology. We present a novel system called PhenoLinker capable of associating a score to a phenotype-gene relationship by using heterogeneous…

Graph convolutional networks are a popular class of deep neural network algorithms which have shown success in a number of relational learning tasks. Despite their success, graph convolutional networks exhibit a number of peculiar features,…

A directed graph is semi-transitive if and only if it is acyclic and for any directed path $u_1\rightarrow u_2\rightarrow \cdots \rightarrow u_t$, $t \geq 2$, either there is no edge from $u_1$ to $u_t$ or all edges $u_i\rightarrow u_j$…

We enumerate graph homomorphisms to quasi-complete graphs, i.e., graphs obtained from complete graphs by removing one edge. The source graphs are complete graphs, quasi-complete graphs, cycles, paths, wheels and broken wheels. These…

For a connected graph, a path containing all vertices is known as \emph{Hamiltonian path}. For general graphs, there is no known necessary and sufficient condition for the existence of Hamiltonian paths and the complexity of finding a…

We prove that the degeneracy of graphs in a hereditary class defined by a finite set S of forbidden induced subgraphs is bounded if and only if S includes a complete graph, a complete bipartite graph and a forest.

This work illustrates potentials for recognition within {\em ad hoc} sensor networks if their nodes possess individual inter-related biologically inspired genetic codes. The work takes ideas from natural immune systems protecting organisms…

Evolutionary events such as incomplete lineage sorting and lateral gene transfer constitute major problems for inferring species trees from gene trees, as they can sometimes lead to gene trees which conflict with the underlying species…