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An existence theorem of perfect matching on $k$-partite $k$-uniform hypergraphs via distance spectral radius | ||
Transactions on Combinatorics | ||
مقاله 8، دوره 13، شماره 4، اسفند 2024، صفحه 377-385 اصل مقاله (472.98 K) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22108/toc.2023.137937.2077 | ||
نویسندگان | ||
Lei Zhang؛ Haizhen Ren* | ||
Department of Mathematics and Statistics, Qinghai Normal University, Xining, China | ||
چکیده | ||
Let $n_1, n_2,\ldots,n_k$ be integers and $V_1, V_2,\ldots,V_k$ be disjoint vertex sets with $|V_i|=n_i$ for each $i= 1, 2,\ldots,k$. A $k$-partite $k$-uniform hypergraph on vertex classes $V_1, V_2,\ldots,V_k$ is defined to be the $k$-uniform hypergraph whose edge set consists of the $k$-element subsets $S$ of $V_1 \cup V_2 \cup \cdots \cup V_k$ such that $|S\cap V_i|=1$ for all $i= 1, 2,\ldots,k$. We say that it is balanced if $n_1=n_2=\cdots=n_k$. In this paper, we give a distance spectral radius condition to guarantee the existence of perfect matching in $k$-partite $k$-uniform hypergraphs, this result generalize the result of Zhang and Lin [Perfect matching and distance spectral radius in graphs and bipartite graphs, Discrete Appl. Math., 304 (2021) 315-322]. | ||
کلیدواژهها | ||
$k$-uniform $k$-partite hypergraphs؛ Distance spectral radius؛ Perfect matching | ||
مراجع | ||
[1] M. Aouchiche and P. Hansen, Distance spectra of graphs: A survey, Linear Algebra Appl., 458 (2014) 301–386. [10] R. Karp, Reducibility among combinatorial problems, Complexity of Computer Computations, Springer, Berlin, 1972. | ||
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