Degree-Splittability of Multigraphs and Caterpillars
نویسندگان
چکیده
A multigraph is degree-splittable if it decomposes into two submultigraphs whose degree lists are the same, plus one leftover edge when the total number of edges is odd. We prove that a connected multigraph is degree-splittable if it has an even number of vertices of each odd degree. For caterpillars, we characterize the splittable caterpillars with diameter at most 4, provide a general sufficient condition for splittability of caterpillars, and prove that the smallest maximum degree of a non-splittable caterpillar is 5.
منابع مشابه
On the harmonic index and harmonic polynomial of Caterpillars with diameter four
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