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An outerplanar graph is a planar graph that has a planar drawing with all vertices on the unbounded face. The matching complex of a graph is the simplicial complex whose faces are subsets of disjoint edges of the graph. In this paper we prove that th
Externí odkaz:
http://arxiv.org/abs/2411.04601
Autor:
Aliyev, Fateh, Gladkov, Nikita
We establish a lower bound on the forcing numbers of domino tilings computable in polynomial time based on height functions. This lower bound is sharp for a 2n by 2n square as well as other cases.
Comment: 10 pages, 4 figures
Comment: 10 pages, 4 figures
Externí odkaz:
http://arxiv.org/abs/2410.23621
Autor:
Paul, Pravakar, Saikia, Manjil P.
In this paper, we give inductive sum formulas to calculate the number of diagonally symmetric, and diagonally \& anti-diagonally symmetric domino tilings of Aztec Diamonds. As a byproduct, we also find such a formula for the unrestricted case as well
Externí odkaz:
http://arxiv.org/abs/2410.23324
Autor:
De Loera, Javier
For cluster algebras of surface type, Musiker, Schiffler and Williams gave a formula for cluster variables in terms of perfect matchings of snake graphs. Building on this, we provide a simple determinantal formula for cluster variables via the weight
Externí odkaz:
http://arxiv.org/abs/2410.14554
We prove a conjecture of Gy\'arf\'as (1976), which asserts that any family of trees $T_1, \dots, T_{n}$ where each $T_k$ has $k$ vertices packs into $K_n$. We do so by translating the decomposition problem into a labeling problem, namely complete lab
Externí odkaz:
http://arxiv.org/abs/2410.13840
Autor:
Zhou, Sizhong
Let $G$ denote a graph and $k\geq2$ be an integer. A $\{K_{1,1},K_{1,2},\ldots,K_{1,k},\mathcal{T}(2k+1)\}$-factor of $G$ is a spanning subgraph, whose every connected component is isomorphic to an element of $\{K_{1,1},K_{1,2},\ldots,K_{1,k},\mathca
Externí odkaz:
http://arxiv.org/abs/2410.06829
Autor:
Minyard, Mitchell, Sepanski, Mark R.
A graph is said to be neighborhood 3-balanced if there exists a vertex labeling with three colors so that each vertex has an equal number of neighbors of each color. We give order constraints on 3-balanced graphs, determine which generalized Petersen
Externí odkaz:
http://arxiv.org/abs/2410.05422
Autor:
Mkrtchyan, Vahan
Let $Z_2\times Z_2=\{0, \alpha, \beta, \alpha+\beta\}$. If $G$ is a bridgeless cubic graph, $F$ is a perfect matching of $G$ and $\overline{F}$ is the complementary 2-factor of $F$, then a no-where zero $Z_2\times Z_2$-flow $\theta$ of $G/\overline{F
Externí odkaz:
http://arxiv.org/abs/2410.04389
The fractional list packing number $\chi_{\ell}^{\bullet}(G)$ of a graph $G$ is a graph invariant that has recently arisen from the study of disjoint list-colourings. It measures how large the lists of a list-assignment $L:V(G)\rightarrow 2^{\mathbb{
Externí odkaz:
http://arxiv.org/abs/2410.02695
In 1992, Erd\H{o}s and Hajnal posed the following natural problem: Does there exist, for every $r\in \mathbb{N}$, an integer $F(r)$ such that every graph with chromatic number at least $F(r)$ contains $r$ edge-disjoint cycles on the same vertex set?
Externí odkaz:
http://arxiv.org/abs/2410.02437