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Offline, standard-library-only verification software accompanying Seth Christopher's preprint “A Split-Graph Counterexample to a Roman–Double Roman Candidate Inequality”. Version 1.0.0; source-only publication revision figshare.1. This item contains Roman_Double_Roman_Verification_Software_v1.0.0.zip, including the byt...
This preprint combines three investigations of independent sets on finite trees. It proves arbitrarily long consecutive blocks of strict log-concavity failures in a fixed family of unweighted subcubic trees. For every fixed positive epsilon less than one, a suitable fixed terminal path gives at least a constant multipl...
Offline, standard-library-only verification software accompanying Seth Christopher's preprint “A Split-Graph Counterexample to a Roman–Double Roman Candidate Inequality”. Version 1.0.0; source-only publication revision figshare.1. This item contains Roman_Double_Roman_Verification_Software_v1.0.0.zip, including the byt...
Offline verification software accompanying Seth Christopher's preprint “Roman Labels Yield One-Round Power Domination”. Scientific version 1.0.0; packaging revision figshare.2. All 24 Python files are byte-identical to figshare.1. The README, release metadata and checksum manifest have been updated; historical versions...
We give a connected chordal graph on 15 vertices and 30 edges with Roman domination number 7 and double Roman domination number 10. It refutes the candidate inequality (3/2) gamma_R(G) <= gamma_dR(G) recorded at rank 67 of AutoGraphForge's public audit, together with its equivalent rank-68 restatement. The graph consis...
We give a connected chordal graph on 15 vertices and 30 edges with Roman domination number 7 and double Roman domination number 10. It refutes the candidate inequality (3/2) gamma_R(G) <= gamma_dR(G) recorded at rank 67 of AutoGraphForge's public audit, together with its equivalent rank-68 restatement. The graph consis...
We construct a connected graph on 15 vertices with burning number 4 and Slater number 2, refuting the candidate inequality b(G) <= s(G) + 1 recorded in AutoGraphForge's public conjecture audit. The graph consists of a clique K7 joined by one edge to a path on eight new vertices. Its Slater number is determined by its t...
This preprint proves that, for every finite simple graph without isolated vertices, the power domination number is at most half the Roman domination number, rounded down. More strongly, any Roman dominating function of weight w yields a sensor set of size at most floor(w/2) that observes the graph after initial dominat...
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