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Degree-balanced decompositions of cubic graphs
Borut Lužar, Jakub Przybyło, Roman Soták
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Oznake: irregular subgraph;repeated degrees;degree-balanced decomposition;
We show that every cubic graph on ▫$n$▫ vertices contains a spanning subgraph, in which the number of vertices of each degree deviates from ▫$\frac{n}{4}$▫ by at most ▫$\frac{1}{2}$▫, up to three exceptions. This resolves the conjecture of Alon and Wei ({\em Irregular subgraphs, Combin. Probab. Comp ...
Leto: 2025 Vir: Fakulteta za informacijske študije v Novem mestu (FIŠ)
List strong and list normal edge-coloring of (sub)cubic graphs
Borut Lužar, Edita Máčajová, Roman Soták, Diana Švecová
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Oznake: strong edge-coloring;list strong edge-coloring;normal edge-coloring;list normal edge-coloring;Petersen coloring;Petersen coloring conjecture;
A ▫${\ strong edge-coloring}$▫ of a graph is a proper edge-coloring, in which the edges of every path of length ▫$3$▫ receive distinct colors; in other words, every pair of edges at distance at most ▫$2$▫ must be colored differently. The least number of colors needed for a strong edge-coloring of a ...
Leto: 2026 Vir: Fakulteta za informacijske študije v Novem mestu (FIŠ)
Št. zadetkov: 2
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