Related papers: Subgraphs of 4-regular planar graphs
Subgraph and homomorphism counting are fundamental algorithmic problems. Given a constant-sized pattern graph $H$ and a large input graph $G$, we wish to count the number of $H$-homomorphisms/subgraphs in $G$. Given the massive sizes of…
We prove that there is an algorithm to determine if a given finite graph is an induced subgraph of a given curve graph.
The Subgraph Isomorphism problem is of considerable importance in computer science. We examine the problem when the pattern graph H is of bounded treewidth, as occurs in a variety of applications. This problem has a well-known algorithm via…
A graph is called 1-planar if there exists its drawing in the plane such that each edge is crossed at most once. In this paper, we study 1-planar graph joins. We prove that the join $G+H$ is 1-planar if and only if the pair $[G,H]$ is…
Given a family $\mathcal{F}$ of graphs, a graph is \emph{$\mathcal{F}$-subgraph-free} if it has no subgraph isomorphic to a member of $\mathcal{F}$. We present a fixed-parameter linear-time algorithm that decides whether a planar graph can…
The problem Cover(H) asks whether an input graph G covers a fixed graph H (i.e., whether there exists a homomorphism G to H which locally preserves the structure of the graphs). Complexity of this problem has been intensively studied. In…
In the standard CONGEST model for distributed network computing, it is known that "global" tasks such as minimum spanning tree, diameter, and all-pairs shortest paths, consume large bandwidth, for their running-time is…
A 4-wheel is a graph formed by a cycle C and a vertex not in C that has at least four neighbors in C. We prove that a graph G that does not contain a 4-wheel as a subgraph is 4-colorable and we describe some structural properties of such a…
A geometric graph is a drawing of a graph in the plane where the vertices are drawn as points in general position and the edges as straight-line segments connecting their endpoints. It is plane if it contains no crossing edges. We study…
Given an undirected graph $G$, the problem of deciding whether $G$ admits a simple and proper time-labeling that makes it temporally connected is known to be NP-hard (G\"obel et al., 1991). In this article, we relax this problem and ask…
We present the first truly subcubic, combinatorial algorithm for detecting an induced $4$-cycle in a graph. The running time is $O(n^{2.84})$ on $n$-node graphs, thus separating the task of detecting induced $4$-cycles from detecting…
Let $\partial_H(u)$ be the set of edges incident with a vertex $u$ in the graph $H$. We say that a graph $G$ is $H$-colorable if there exist total functions $f : E(G) \rightarrow E(H)$ and $g : V(G) \rightarrow V(H)$ such that $f$ is a…
A graph $G$ is almost hypohamiltonian (a.h.) if $G$ is non-hamiltonian, there exists a vertex $w$ in $G$ such that $G - w$ is non-hamiltonian, and $G - v$ is hamiltonian for every vertex $v \ne w$ in $G$. The second author asked in [J.…
In \emph{smooth orthogonal layouts} of planar graphs, every edge is an alternating sequence of axis-aligned segments and circular arcs with common axis-aligned tangents. In this paper, we study the problem of finding smooth orthogonal…
We show that deciding whether a given graph $G$ of size $m$ has a unique perfect matching as well as finding that matching, if it exists, can be done in time $O(m)$ if $G$ is either a cograph, or a split graph, or an interval graph, or…
The $r$-th iterated line graph $L^{r}(G)$ of a graph $G$ is defined by: (i) $L^{0}(G) = G$ and (ii) $L^{r}(G) = L(L^{(r- 1)}(G))$ for $r > 0$, where $L(G)$ denotes the line graph of $G$. The Hamiltonian Index $h(G)$ of $G$ is the smallest…
A graph $G$ is said to be an $(s, k)$-polar graph if its vertex set admits a partition $(A, B)$ such that $A$ and $B$ induce, respectively, a complete $s$-partite graph and the disjoint union of at most $k$ complete graphs. Polar graphs and…
For a class $\mathcal{G}$ of graphs, the problem SUBGRAPH COMPLEMENT TO $\mathcal{G}$ asks whether one can find a subset $S$ of vertices of the input graph $G$ such that complementing the subgraph induced by $S$ in $G$ results in a graph in…
We present an algorithm for determining whether a bipartite graph $G$ is 2-chordal (formerly doubly chordal bipartite). At its core this algorithm is an extension of the existing efficient algorithm for determining whether a graph is…
It is an intriguing question to see what kind of information on the structure of an oriented graph $D$ one can obtain if $D$ does not contain a fixed oriented graph $H$ as a subgraph. The related question in the unoriented case has been an…