相关论文: Maximal matchings in polyspiro and benzenoid chain…
Maximal green sequences are particular sequences of quiver mutations appearing in the context of quantum dilogarithm identities and supersymmetric gauge theory. Interpreting maximal green sequences as paths in various natural posets arising…
An $n$-poised node set $\mathcal X$ in the plane is called $GC_n$ set if the (bivariate) fundamental polynomial of each node is a product of n linear factors. A line is called $k$-node line if it passes through exactly $k$-nodes of…
The enumeration of perfect matchings of graphs is equivalent to the dimer problem which has applications in statistical physics. A graph $G$ is said to be $n$-rotation symmetric if the cyclic group of order $n$ is a subgroup of the…
For each $b \geq 5$ we construct a pair of cospectral $b$-regular graphs, where one has a perfect matching and the other one not. This solves a research problem posed by the third author at the 22nd British Combinatorial Conference.
EPG graphs, introduced by Golumbic et al. in 2009, are edge-intersection graphs of paths on an orthogonal grid. The class $B_k$-EPG is the subclass of EPG graphs where the path on the grid associated to each vertex has at most $k$ bends.…
Temporal graphs are graphs whose topology is subject to discrete changes over time. Given a static underlying graph $G$, a temporal graph is represented by assigning a set of integer time-labels to every edge $e$ of $G$, indicating the…
Let $G$ be a simple graph that is properly edge coloured with $m$ colours and let $\M=\{M_1,\ldots, M_m\}$ be the set of $m$ matchings induced by the colours in $G$. Suppose that $m\le n-n^{c}$, where $c>9/10$, and every matching in $\M$…
Let $\mathscr{P}_{m}$ be the graph on the set of perfect matchings in the complete graph $K_{2m}$, where two perfect matchings are connected by an edge if their symmetric difference is a cycle of length four. This paper studies geodesics in…
In this paper, we study two problems related to planar matchings in random bipartite graphs. First, we colour each edge of the complete bipartite graph $K_{n,n}$ uniformly randomly from amongst ${r}$ colours and show that if ${r}$ grows…
Suppose that G is a simple, undirected graph. An induced matching in G is a set of edges M in the edge set E(G) of G such that if e1, e2 in M, then no endpoint v1, v2 of e1 and e2 respectively is incident to any edge ek in E(G) such that ek…
Finding maximum-cardinality matchings in undirected graphs is arguably one of the most central graph problems. For general m-edge and n-vertex graphs, it is well-known to be solvable in $O(m \sqrt{n})$ time. We develop a linear-time…
In this paper, we study the maximum matching problem in RDV graphs, i.e., graphs that are vertex-intersection graphs of downward paths in a rooted tree. We show that this problem can be reduced to a problem of testing (repeatedly) whether a…
The maximal chain polytope $\mathscr{M}(P)$ is associated with a finite poset $P$. For a set of maximal chains $\mathcal{C}$, it is shown that the convex hull of all the points corresponding to elements of $\mathcal{C}$ is not a face of…
In this paper, two recursion formulae of chromatic polynomial of a maximal planar graph G are obtained. Moreover, the application of these formulaes to the proof of Four-Color Conjecture is investigated. By using these formulae, the proof…
In connection with Fulkerson's conjecture on cycle covers, Fan and Raspaud proposed a weaker conjecture: For every bridgeless cubic graph $G$, there are three perfect matchings $M_1$, $M_2$, and $M_3$ such that $M_1\cap M_2 \cap…
Asymptotic properties of random regular graphs are object of extensive study in mathematics. In this note we argue, based on theory of spin glasses, that in random regular graphs the maximum cut size asymptotically equals the number of…
In this paper, we study the non-bipartite maximum matching problem in the semi-streaming model. The maximum matching problem in the semi-streaming model has received a significant amount of attention lately. While the problem has been…
For a finite graph $G$, we study the maximum $2$-edge colorable subgraph problem and a related ratio $\frac{\mu(G)}{\nu(G)}$, where $\nu(G)$ is the matching number of $G$, and $\mu(G)$ is the size of the largest matching in any pair…
The number of proper $q$-colorings of a graph $G$, denoted by $P_G(q)$, is an important graph parameter that plays fundamental role in graph theory, computational complexity theory and other related fields. We study an old problem of Linial…
In the Matching Cut problem we ask whether a graph $G$ has a matching cut, that is, a matching which is also an edge cut of $G$. We consider the variants Perfect Matching Cut and Disconnected Perfect Matching where we ask whether there…