Open Access
February, 2018 Pack Graphs with Subgraphs of Size Three
Zhen-Chun Chen, Hung-Lin Fu, Kuo-Ching Huang
Taiwanese J. Math. 22(1): 1-15 (February, 2018). DOI: 10.11650/tjm/8093


An $H$-packing $\mathcal{F}$ of a graph $G$ is a set of edge-disjoint subgraphs of $G$ in which each subgraph is isomorphic to $H$. The leave $L$ or the remainder graph $L$ of a packing $\mathcal{F}$ is the subgraph induced by the set of edges of $G$ that does not occur in any subgraph of the packing $\mathcal{F}$. If a leave $L$ contains no edges, or simply $L = \phi$, then $G$ is said to be $H$-decomposable, denoted by $H \mid G$. In this paper, we prove a conjecture made by Chartrand, Saba and Mynhardt [13]: If $G$ is a graph of size $q(G) \equiv 0 \pmod{3}$ and $\delta(G) \geq 2$, then $G$ is $H$-decomposable for some graph $H$ of size $3$.


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Zhen-Chun Chen. Hung-Lin Fu. Kuo-Ching Huang. "Pack Graphs with Subgraphs of Size Three." Taiwanese J. Math. 22 (1) 1 - 15, February, 2018.


Received: 20 July 2016; Revised: 5 January 2017; Accepted: 20 April 2017; Published: February, 2018
First available in Project Euclid: 17 August 2017

zbMATH: 06965355
MathSciNet: MR3749350
Digital Object Identifier: 10.11650/tjm/8093

Primary: 05C51 , 05C71

Keywords: $H$-decomposition , $H$-packing , graph decomposition , maximum packing , minimum leave , Packing

Rights: Copyright © 2018 The Mathematical Society of the Republic of China

Vol.22 • No. 1 • February, 2018
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