一个与平衡方程相关的重构问题-- I
A reconstruction problem related to balance equations-I
摘要：
通过以所有可能的方式移除$k$边并以所有可能的方式添加$k$（不一定是新的）边来获得图的修改的$k$ -甲板。Krasikov和Roditty使用这些卡片对Müller关于图的边可重构性的结果给出了独立的证明。他们询问是否可以从其改进的$k$ -甲板上建造一个$k$ -边缘甲板。在本文中，我们解决了这个问题时，$k=1$。我们还提供了新的证明Lovász的结果，一个明确地描述所构造的图，（从而回答了一个问题的邦迪），另一个基于约翰逊图的特征值。
英文摘要：
A modified $k$-deck of a graph is obtained by removing $k$ edges in all possible ways and adding $k$ (not necessarily new) edges in all possible ways. Krasikov and Roditty used these decks to give an independent proof of Müller's result on the edge reconstructibility of graphs. They asked if a $k$-edge deck could be constructed from its modified $k$-deck. In this paper, we solve the problem when $k=1$. We also offer new proofs of Lovász's result, one describing the constructed graph explicitly, (thus answering a question of Bondy), and another based on the eigenvalues of Johnson graph.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
