Opuscula Math. 37, no. 3 (2017), 435-446
http://dx.doi.org/10.7494/OpMath.2017.37.3.435

 
Opuscula Mathematica

On strongly spanning k-edge-colorable subgraphs

Vahan V. Mkrtchyan
Gagik N. Vardanyan

Abstract. A subgraph \(H\) of a multigraph \(G\) is called strongly spanning, if any vertex of \(G\) is not isolated in \(H\). \(H\) is called maximum \(k\)-edge-colorable, if \(H\) is proper \(k\)-edge-colorable and has the largest size. We introduce a graph-parameter \(sp(G)\), that coincides with the smallest \(k\) for which a multigraph \(G\) has a maximum \(k\)-edge-colorable subgraph that is strongly spanning. Our first result offers some alternative definitions of \(sp(G)\). Next, we show that \(\Delta(G)\) is an upper bound for \(sp(G)\), and then we characterize the class of multigraphs \(G\) that satisfy \(sp(G)=\Delta(G)\). Finally, we prove some bounds for \(sp(G)\) that involve well-known graph-theoretic parameters.

Keywords: \(k\)-edge-colorable subgraph, maximum \(k\)-edge-colorable subgraph, strongly spanning \(k\)-edge-colorable subgraph, \([1,k]\)-factor.

Mathematics Subject Classification: 05C70, 05C15.

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  • Vahan V. Mkrtchyan
  • Yerevan State University, Department of Informatics and Applied Mathematics, Yerevan, 0025, Armenia
  • National Academy of Sciences of Republic of Armenia, Institute for Informatics and Automation Problems, 0014, Armenia
  • Gagik N. Vardanyan
  • Yerevan State University, Department of Informatics and Applied Mathematics, Yerevan, 0025, Armenia
  • Communicated by Mariusz Meszka.
  • Received: 2015-12-03.
  • Revised: 2016-09-15.
  • Accepted: 2016-09-29.
  • Published online: 2017-01-30.
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Cite this article as:
Vahan V. Mkrtchyan, Gagik N. Vardanyan, On strongly spanning k-edge-colorable subgraphs, Opuscula Math. 37, no. 3 (2017), 435-446, http://dx.doi.org/10.7494/OpMath.2017.37.3.435

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