Related papers: Parking functions and chip-firing on hypergraphs

Let $G=(V,E)$ and $H$ be two graphs. Packing problem is to find in $G$ the largest number of independent subgraphs each of which is isomorphic to $H$. Let $U\subset{V}$. If the graph $G-U$ has no subgraph isomorphic to $H$, $U$ is a cover…

The weak minor G of a graph G is the graph obtained from G by a sequence of edge-contraction operations on G. A weak-minor-closed family of upper embeddable graphs is a set G of upper embeddable graphs that for each graph G in G, every weak…

Consider the vector space $\mathbb{K}\mathcal{P}$ spanned by parking functions. By representing parking functions as labeled digraphs, Hivert, Novelli and Thibon constructed a cocommutative Hopf algebra PQSym$^{*}$ on…

Given a hypergraph $H$, the Planar Support problem asks whether there is a planar graph $G$ on the same vertex set as $H$ such that each hyperedge induces a connected subgraph of $G$. Planar Support is motivated by applications in graph…

Given an undirected graph $G = (V_G, E_G)$ and a fixed "pattern" graph $H = (V_H, E_H)$ with $k$ vertices, we consider the $H$-Transversal and $H$-Packing problems. The former asks to find the smallest $S \subseteq V_G$ such that the…

We present an algorithm to count the number of occurrences of a pattern graph $H$ as an induced subgraph in a host graph $G$. If $G$ belongs to a bounded expansion class, the algorithm runs in linear time. Our design choices are motivated…

We consider the $H$-Induced Minor problem: for a fixed graph~$H$, decide whether a given graph $G$ contains $H$ as an induced minor. While the problem is known to be NP-complete for some trees~$H$ on more than $2^{300}$ vertices, the…

Algorithms for listing the subgraphs satisfying a given property (e.g.,being a clique, a cut, a cycle, etc.) fall within the general framework of set systems. A set system (U, F) uses a ground set U (e.g., the network nodes) and an…

We study a class of aggregate-join queries with multiple aggregation operators evaluated over annotated relations. We show that straightforward extensions of standard multiway join algorithms and generalized hypertree decompositions (GHDs)…

A classical parking function of length $n$ is a list of positive integers $(a_1, a_2, \ldots, a_n)$ whose nondecreasing rearrangement $b_1 \leq b_2 \leq \cdots \leq b_n$ satisfies $b_i \leq i$. The convex hull of all parking functions of…

We consider questions related to the existence of spanning trees in graphs with the property that after the removal of any path in the tree the graph remains connected. We show that, for planar graphs, the existence of trees with this…

Let $G=(V,E)$ be a graph. An ordering of $G$ is a bijection $\alpha: V\dom \{1,2,..., |V|\}.$ For a vertex $v$ in $G$, its closed neighborhood is $N[v]=\{u\in V: uv\in E\}\cup \{v\}.$ The profile of an ordering $\alpha$ of $G$ is…

Given a graph $G$, we define ${\bf bcg}(G)$ as the minimum $k$ for which $G$ can be contracted to the uniformly triangulated grid $\Gamma_{k}$. A graph class ${\cal G}$ has the SQG${\bf C}$ property if every graph $G\in{\cal G}$ has…

For each skew shape we define a nonhomogeneous symmetric function, generalizing a construction of Pak and Postnikov. In two special cases, we show that the coefficients of this function when expanded in the complete homogeneous basis are…

For graphs $G$ and $H$, an $H$-coloring of $G$ is an adjacency preserving map from the vertices of $G$ to the vertices of $H$. $H$-colorings generalize such notions as independent sets and proper colorings in graphs. There has been much…

A vertex whose removal in a graph $G$ increases the number of components of $G$ is called a cut vertex. For all $n,c$, we determine the maximum number of connected induced subgraphs in a connected graph with order $n$ and $c$ cut vertices,…

Here we review the many aspects and distinct phenomena associated to quantum dynamics on general graph structures. For so, we discuss such class of systems under the energy domain Green's function ($G$) framework. This approach is…

Let G and H be two cographs. We show that the problem to determine whether H is a retract of G is NP-complete. We show that this problem is fixed-parameter tractable when parameterized by the size of H. When restricted to the class of…

We consider the notion of classical parking functions by introducing randomness and a new parking protocol, as inspired by the work presented in the paper ``Parking Functions: Choose your own adventure,'' (arXiv:2001.04817) by Carlson,…

For integer q>1, we derive edge q-colouring models for (i) the Tutte polynomial of a graph G on the hyperbola H_q, (ii) the symmetric weight enumerator of the set of group-valued q-flows of G, and (iii) a more general vertex colouring model…