IJPAM: Volume 101, No. 5 (2015)

ACYCLIC EDGE-COLORING OF HYPERTREE
AND SHUFFLE HYPERTREE

D. Paul$^1$, Indra Rajasingh$^2$, R. Sundara Rajan$^3$
$^{1,2,3}$School of Advanced Sciences
VIT University
Chennai, INDIA


Abstract. An acyclic edge-coloring of a graph is a proper edge-coloring such that there are no bichromatic cycles. The acyclic chromatic index of a graph $G$ is the minimum number $k$ such that there is an acyclic edge-coloring using $k$ colors and is denoted by $\chi_a'(G)$. The maximum degree in $G$ denoted by $\Delta(G)$, is the lower bound for $\chi_a'(G)$. We have introduced an architecture called Shuffle hypertree which is a variation of an hypertree. $T$-cuts introduced in this paper acts as a powerful tool to prove that this bound is sharp for hypertree and Shuffle hypertree.

Received: March 12, 2015

AMS Subject Classification: 05C15

Key Words and Phrases: acyclic edge-coloring; acyclic chromatic index; maximum degree; hypertree; Shuffle hypertree

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DOI: 10.12732/ijpam.v101i5.3 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2015
Volume: 101
Issue: 5
Pages: 623 - 629


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