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The generalized $k$-connectivity of a graph $G$, denoted by $\kappa_k(G)$, is the minimum number of internally edge disjoint $S$-trees for any $S\subseteq V(G)$ and $|S|=k$. The generalized $k$-connectivity is a natural extension of the classical con
Externí odkaz:
http://arxiv.org/abs/2405.15147
The generalized $k$-connectivity of a graph $G$, denoted by $\kappa_k(G)$, is the minimum number of internally edge disjoint $S$-trees for any $S\subseteq V(G)$ and $|S|=k$. The generalized $k$-connectivity is a natural extension of the classical con
Externí odkaz:
http://arxiv.org/abs/2310.00878
A matching of a graph is a set of edges without common end vertex. A graph is called 1-planar if it admits a drawing in the plane such that each edge is crossed at most once. Recently, Biedl and Wittnebel proved that every 1-planar graph with minimum
Externí odkaz:
http://arxiv.org/abs/2207.03747
Publikováno v:
In Discrete Applied Mathematics 15 January 2025 360:93-114
Publikováno v:
Applied Math and computation 415 (2021), 126697
It is well-known that the number of spanning trees, denoted by $\tau(G)$, in a connected multi-graph $G$ can be calculated by the Matrix-Tree theorem and Tutte's deletion-contraction theorem. In this short note, we find an alternate method to compute
Externí odkaz:
http://arxiv.org/abs/2106.07871
A graph is called $1$-planar if it admits a drawing in the plane such that each edge is crossed at most once. Let $G$ be a bipartite 1-planar graph with $n$ ($\ge 4$) vertices and $m$ edges. Karpov showed that $m\le 3n-8$ holds for even $n\ge 8$ and
Externí odkaz:
http://arxiv.org/abs/2007.13308
A graph $G$ is {$k$-crossing-critical} if $cr(G)\ge k$, but $cr(G\setminus e)
Externí odkaz:
http://arxiv.org/abs/2003.06579
The chromatic polynomial $P(G,x)$ of a graph $G$ of order $n$ can be expressed as $\sum\limits_{i=1}^n(-1)^{n-i}a_{i}x^i$, where $a_i$ is interpreted as the number of broken-cycle free spanning subgraphs of $G$ with exactly $i$ components. The parame
Externí odkaz:
http://arxiv.org/abs/1803.08658
Publikováno v:
In Discrete Mathematics December 2022 345(12)
Publikováno v:
In Applied Mathematics and Computation 15 February 2022 415