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arXiv · 2308.11613

Ascending Subgraph Decomposition

Kyriakos Katsamaktsis·Shoham Letzter·Alexey Pokrovskiy·Benny Sudakov
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Abstract

A typical theme for many well-known decomposition problems is to show that some obvious necessary conditions for decomposing a graph $G$ into copies $H_1, \ldots, H_m$ are also sufficient. One such problem was posed in 1987, by Alavi, Boals, Chartrand, Erdős, and Oellerman. They conjectured that the edges of every graph with $\binom{m+1}2$ edges can be decomposed into subgraphs $H_1, \dots, H_m$ such that each $H_i$ has $i$ edges and is isomorphic to a subgraph of $H_{i+1}$. In this paper we prove this conjecture for sufficiently large $m$.

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Kyriakos Katsamaktsis, Shoham Letzter, Alexey Pokrovskiy, Benny Sudakov. 2023-09-05. Ascending Subgraph Decomposition. https://arxiv.org/abs/2308.11613

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