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On a star chromatic index of subcubic graphs [Elektronski vir]Lužar, Borut ; Mockovčiaková, Martina ; Soták, RomanA vertex signature ▫$\pi$▫ of a finite graph ▫$G$▫ is any mapping ▫$\pi \, : \, V(G)\to \{0,1\}$▫. An edge-coloring of ▫$G$▫ is said to be \textit{vertex-parity} for the pair ▫$(G,\pi)$▫ if for every ... vertex ▫$v$▫ each color used on the edges incident to ▫$v$▫ appears in parity accordance with ▫$\pi$▫, i.e. an even or odd number of times depending on whether ▫$\pi(v)$▫ equals ▫$0$▫ or ▫$1$▫, respectively. The minimum number of colors for which ▫$(G,\pi)$▫ admits such an edge-coloring is denoted by ▫$\chi'_p(G,\pi)$▫. We characterize the existence and prove that ▫$\chi'_p(G,\pi)$▫ is at most ▫$6$▫. Furthermore, we give a structural characterization of the pairs ▫$(G,\pi)$▫ for which ▫$\chi'_p(G,\pi)=5$▫ and ▫$\chi'_p(G,\pi)=6$▫. In the last part of the paper, we consider a weaker version of the coloring, where it suffices that at every vertex, at least one color appears in parity accordance with $\pi$. We show that the corresponding chromatic index is at most ▫$3$▫ and give a complete characterization for it.Source: The European Conference on Combinatorics, Graph Theory and Applications, (EUROCOMBʼ17), TU Vienna, Vienna, August 28 - September 1, 2017 [Elektronski vir] (Vol. 61, 2017, str. 835-839)Type of material - conference contribution ; adult, seriousPublish date - 2017Language - englishCOBISS.SI-ID - 2048470547
Author
Lužar, Borut |
Mockovčiaková, Martina |
Soták, Roman
Topics
vozliščno-parnostno barvanje povezav |
vozliščno-parnostni kromatični indeks |
šibko vozliščno-parnostno barvanje povezav |
predznačenje vozlišč |
vertex-parity edge-coloring |
vertex-parity chromatic index |
weak vertex-parity edge-coloring |
vertex signature
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Database name | Field | Year |
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Lužar, Borut | 31670 |
Mockovčiaková, Martina | |
Soták, Roman | 36239 |
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