Consider L^i(T) is a graph with "even triangle"(triangle with even degrees of vertices) subgraph. Edges of even triangle produce new even triangle in L^(i+1)(T). And if there is an odd degree vertex adjacent to parent triangle, there would be another one adjacent to child. So, irregular subgraph remains.
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CSI of Charles University
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Consider L^i(T) is a graph with "even triangle"(triangle with even degrees of vertices) subgraph. Edges of even triangle produce new even triangle in L^(i+1)(T). And if there is an odd degree vertex adjacent to parent triangle, there would be another one adjacent to child. So, irregular subgraph remains.