On the complexity of finding large odd induced subgraphs and odd colorings - LIRMM - Laboratoire d’Informatique, de Robotique et de Microélectronique de Montpellier Access content directly
Journal Articles Algorithmica Year : 2021

On the complexity of finding large odd induced subgraphs and odd colorings

Ignasi Sau

Abstract

We study the complexity of the problems of finding, given a graph G, a largest induced subgraph of G with all degrees odd (called an odd subgraph), and the smallest number of odd subgraphs that partition V (G). We call these parameters mos(G) and χ odd (G), respectively. We prove that deciding whether χ odd (G) ≤ q is polynomial-time solvable if q ≤ 2, and NP-complete otherwise. We provide algorithms in time 2 O(rw) •n O(1) and 2 O(q•rw) •n O(1) to compute mos(G) and to decide whether χ odd (G) ≤ q on n-vertex graphs of rank-width at most rw, respectively, and we prove that the dependency on rank-width is asymptotically optimal under the ETH. Finally, we give some tight bounds for these parameters on restricted graph classes or in relation to other parameters.
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Dates and versions

lirmm-03374591 , version 1 (12-10-2021)

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Rémy Belmonte, Ignasi Sau. On the complexity of finding large odd induced subgraphs and odd colorings. Algorithmica, 2021, 83 (8), pp.2351-2373. ⟨10.1007/s00453-021-00830-x⟩. ⟨lirmm-03374591⟩
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